Tutors Answer Your Questions about Linear-systems (FREE)
Question 1123099: Solve By Elimination:
Roast beef has 25 grams of protein and 11 grams of calcium per serving. A serving of mashed potatoes has 2 grams of protein and 25 grams of calcium. How many servings of each are needed to supply exactly 29 grams of protein and 61 grams of calcium? Use b for servings of beef and m for servings of mashed potatoes.
Click here to see answer by ikleyn(52786)   |
Question 1123101: A worker received a $10,000 bonus and decided to split it among three different accounts. He placed part in a savings account paying 4.5% per year, twice as much in government bonds paying 5%, and the rest in a mutual fund that returned 4%. His income from these investments after one year was $455. How much did the worker place in each account? Solve by showing an input matrix and solution matrix.
*I know how to put the matrix into the calculator, but I do not know what the numbers are that go in the matrix for this word problem.
Click here to see answer by ikleyn(52786) |
Question 1123198: 1. The Alpha Furniture Company manufactures dining room tables and chairs. Each table requires 50 board feet and 3 hours of labor. Each chair takes 20 board feet and 4 hours of labor. The manufacturer has 3,300 board feet of lumber available and a staff able to provide 380 hours of labor. Finally, the manufacturer has determined that there is a net profit of P100 for each chair sold and P200 for every table sold. For simplicity, we assume that needed materials (such as nails and varnish) are available in sufficient quantities. How many tables and chairs should the company manufacture in order to maximize its profits, assuming that each item manufactured is sold?
2. A small petroleum company owns two refineries. Refinery 1 costs $20,000 per day to operate, and it can produce 400 barrels of high-grade oil, 300 barrels of medium-grade oil, and 200 barrels of low-grade oil each day. Refinery 2 is newer and more modern. It costs $25,000 per day to operate, and it can produce 300 barrels of high-grade oil, 400 barrels of medium-grade oil, and 500 barrels of low-grade oil each day. The company has orders totaling 25,000 barrels of high-grade oil, 27,000 barrels of medium-grade oil, and 30,000 barrels of low-grade oil. How many days should it run each refinery to minimize its costs and still refine enough oil to meet its orders?
3. A steel company has two mills. Mill 1 costs $70,000 per day to operate, and it can produce 400 tons of high-grade steel, 500 tons of medium-grade steel, and 450 tons of low-grade steel each day. Mill 2 costs $60,000 per day to operate, and it can produce 350 tons of high-grade steel, 600 tons of medium-grade steel, and 400 tons of low-grade steel each day. The company has orders totaling 100,000 tons of high-grade steel, 150,000 tons of medium-grade steel, and 124,500 tons of low-grade steel. How many days should the company run each mill to minimize its costs and still fill the orders?
4. A western shop wishes to purchase 300 felt and 200 straw cowboy hats. Bids have been received from the wholesalers. Beta Hatters has agreed to supply not more than 200 hats, Kappa Hatters not more than 250, Delta Hatters nor more than 150. The owner of the shop has estimated that his profit per hat sold for Beta Hatters would be P30/felt and P40/straw, from Kappa Hatters P38/felt and P35/straw, and from Delta Hatters P40/felt and P36/straw. Set up a linear programming to maximize the owner’s profit.
Click here to see answer by ikleyn(52786) |
Question 1123198: 1. The Alpha Furniture Company manufactures dining room tables and chairs. Each table requires 50 board feet and 3 hours of labor. Each chair takes 20 board feet and 4 hours of labor. The manufacturer has 3,300 board feet of lumber available and a staff able to provide 380 hours of labor. Finally, the manufacturer has determined that there is a net profit of P100 for each chair sold and P200 for every table sold. For simplicity, we assume that needed materials (such as nails and varnish) are available in sufficient quantities. How many tables and chairs should the company manufacture in order to maximize its profits, assuming that each item manufactured is sold?
2. A small petroleum company owns two refineries. Refinery 1 costs $20,000 per day to operate, and it can produce 400 barrels of high-grade oil, 300 barrels of medium-grade oil, and 200 barrels of low-grade oil each day. Refinery 2 is newer and more modern. It costs $25,000 per day to operate, and it can produce 300 barrels of high-grade oil, 400 barrels of medium-grade oil, and 500 barrels of low-grade oil each day. The company has orders totaling 25,000 barrels of high-grade oil, 27,000 barrels of medium-grade oil, and 30,000 barrels of low-grade oil. How many days should it run each refinery to minimize its costs and still refine enough oil to meet its orders?
3. A steel company has two mills. Mill 1 costs $70,000 per day to operate, and it can produce 400 tons of high-grade steel, 500 tons of medium-grade steel, and 450 tons of low-grade steel each day. Mill 2 costs $60,000 per day to operate, and it can produce 350 tons of high-grade steel, 600 tons of medium-grade steel, and 400 tons of low-grade steel each day. The company has orders totaling 100,000 tons of high-grade steel, 150,000 tons of medium-grade steel, and 124,500 tons of low-grade steel. How many days should the company run each mill to minimize its costs and still fill the orders?
4. A western shop wishes to purchase 300 felt and 200 straw cowboy hats. Bids have been received from the wholesalers. Beta Hatters has agreed to supply not more than 200 hats, Kappa Hatters not more than 250, Delta Hatters nor more than 150. The owner of the shop has estimated that his profit per hat sold for Beta Hatters would be P30/felt and P40/straw, from Kappa Hatters P38/felt and P35/straw, and from Delta Hatters P40/felt and P36/straw. Set up a linear programming to maximize the owner’s profit.
Click here to see answer by MathTherapy(10552)  |
Question 1123238: John earned a total of $988 in simple interest from two separate accounts. In an account earning 6% interest, John invested $1,300 more than five times the amount he invested in an account earning 5%. How much did he invest in each account?
Click here to see answer by Boreal(15235)  |
Question 1123253: The average value of a certain type of automobile was $13,140 in 2007 and depreciated to $4740 in 2010. Let y be the average value of the automobile in the year x, where x = 0 represents 2007. Write a linear equation that models the value of the automobile in terms of the year x.
I need help solving this.
Click here to see answer by josgarithmetic(39617) |
Question 1123762: So I was absent at school today so I missed an Algebra lesson. We are learning how we can solve word problems with one/two let statements. Let statements are very familiar to me but they left my mind as the new school year began. Here's my math problem. "The sum of twice a number and 4 is -22. Find the number." I can solve this no problem I just need the let statement(s). Thank you so much for your help if anyone responds!
Click here to see answer by Theo(13342)  |
Question 1123762: So I was absent at school today so I missed an Algebra lesson. We are learning how we can solve word problems with one/two let statements. Let statements are very familiar to me but they left my mind as the new school year began. Here's my math problem. "The sum of twice a number and 4 is -22. Find the number." I can solve this no problem I just need the let statement(s). Thank you so much for your help if anyone responds!
Click here to see answer by MathTherapy(10552) |
Question 1123725: APEX Company produces and sells three products: X, Y and Z. In order to produce them, the company needs to purchase four raw materials A, B, C and D. The prices of these four raw materials are $15/kg, $20/kg, $25/kg and $10/kg, respectively. Each month, the company has a limited budget of $50,000 to buy the raw materials. Producing one X requires 200g of A, 500g of C and 400g of D. Producing one Y requires 500g of A, 800g of B and 700g of C. Producing one Z requires 200g of A, 300g of B, 300g of C and 400g of D. The selling price of each product is based on the cost of raw materials: the profit margins of X, Y, and Z are 20%, 10%, and 25%, respectively.
From past historical data, the manager knows that due to economic situation, the monthly production of X and Z should be capped at 500 and 400 respectively. Besides, the monthly production of Y should be less than two third of the sum of the monthly production of X, Y and Z. Moreover, the monthly production of each product should be at least 100.
(a) Based on the given scenario above, develop a linear programming model to determine the optimal amount of products that the company should produce each month so that its profit is maximized. State your own assumptions and write the objective function and constraints clearly. (10 marks)
(b) Use Excel solver to solve the problem. Note down Answer Report and Sensitivity Report. Based on the report(s), identify the optimal solution and explain which constraints are binding and which are not. (5 marks)
(c) Interpret the sensitivity report from solver and discuss the following scenarios (without re-solving it using Excel Solver). (i) If the monthly budget available is $80,000, how does it affect the optimal profit? If the monthly budget available is $30,000, how does it affect the optimal profit? (4 marks)
(ii) If the profit margin of Y becomes 15% and the profit margin of X becomes 12%, is there a change in the optimal solution? (4 marks)
(d) Discuss how changes in the budget and the selling prices will affect the company’s decisions and profit. (Hint: you need to consider demand.) (12 marks)
Click here to see answer by Theo(13342) |
Question 1124074: The sum of three numbers is 10. The sum of twice the first number, 5 times the second number, and 6 times the third number is 53. The difference between 7 times the first number and the second number is 4.
Find the three numbers.
first number:
second number:
third number:
Click here to see answer by MathLover1(20850)  |
Question 1124075: A person invested $8200 for 1 year, part at 8%, part at 9%, and the remainder at 15%. The total annual income from these investments was $987. The amount of money invested at 15% was $600 more than the amounts invested at 8% and 9% combined. Find the amount invested at each rate.
The person invested $ nothing at 8%,
$nothing at 9%,
and $ nothing at 15%.
Click here to see answer by ikleyn(52786) |
Question 1124614: snajay wants to earn extra money for college. Because he like baking, he decided to sell chocolate chip cookies on campus. The cost to start his business s $120 and each cookie costs 10 cents to make. He will sell the cookies for 50 cents each. How many cookies does he need to sell to break even?
I am a little confused with this question, since we are learning to develop two equations to find the point of intersection. Some help would be great please! I cant figure out what the two equations are supposed to be.
Click here to see answer by math_helper(2461)  |
Question 1124616: Hello, I have used this website before and I found it incredibly useful therefor I would like a little help for one more question if possible:
Darius saved $500 and wants to open a chequing account. Ontario Trust charges $8 per month, plus $0.50 per cheque. Maple Leaf Savings charges $6 per month, plus 0.75 per cheque. Which bank offers the lower monthly charge?
I’m not quite sure if the equations are supposed to be 0.50x + 8y=500 and 0.75x + 8y=500, 0.50x + 8=500 and 0.75x=500, or something completely different. Take your time and thank you for your assistance.
Click here to see answer by MathLover1(20850) |
Question 1124616: Hello, I have used this website before and I found it incredibly useful therefor I would like a little help for one more question if possible:
Darius saved $500 and wants to open a chequing account. Ontario Trust charges $8 per month, plus $0.50 per cheque. Maple Leaf Savings charges $6 per month, plus 0.75 per cheque. Which bank offers the lower monthly charge?
I’m not quite sure if the equations are supposed to be 0.50x + 8y=500 and 0.75x + 8y=500, 0.50x + 8=500 and 0.75x=500, or something completely different. Take your time and thank you for your assistance.
Click here to see answer by ikleyn(52786) |
Question 1124619: Hello! I have used this site Before and it was incredibly useful therefore I was wondering if I can get help for one more question:
Darius saved $500 and wants to open a chequing account. Ontario Trust charges $8 per month, plus $0.50 per cheque. Maple Leaf Savings charges $6 oer month, plus 0.75 per cheque. Which bank offers the lower monthly charge?
It would be great if I can get some help with this, I dont know if the $500 has meaning or if it’s just there to throw you off. Thank you for your time!
Click here to see answer by Boreal(15235) |
Question 1124911: A basic cellular package costs $20 per month for 60 minutes of calling, with an additional charge of $0.20/min beyond that time. The cost formula would be C = 20 + 0.20(x − 60), where C is the cost measured in dollars and x is the number of calling minutes used. If you cannot have a bill greater than $50, what is the maximum number of calling minutes you can use?
Click here to see answer by josgarithmetic(39617) |
Question 1125148: a softball training academy charges student a monthly fee plus an initial registration fee. The total amounts paid by two students are given by the functions f(x)and g(x) where x is the number of months the students have been members of the academy.The graphs of f and g are parallel lines.Did the students pay different monthly fees or different registration fees?How do you know?
Click here to see answer by ankor@dixie-net.com(22740)  |
Question 1125229: In the short run, per capita personal income (PCPI) in the United States grows approximately linearly. In 2009 PCPI was 38.6, and in 2012 it had grown to 42.8 (both in thousands of dollars).
a. Use the two (year,PCPI) data points (1,38.6) and (4, 42.8) to find the linear relationship y=mx+b between x= years since 2008 and y = PCPI.
b. Interpret the slope of the line.
c. Use your linear relationship to predict PCPI in 2020.
Click here to see answer by Boreal(15235) |
Question 1125286: I’m having a hard time understanding what this word problem wants.
“Slope can be thought of as the average rate of change in one quantity per unit change in another. Use the concept of slope to answer the following question: the price of computers has been dropping for the past ten years. If a desktop pc cost $4200 ten years ago, and the same computing power cost $600 two years ago, find the rate of decrease per year. Assume that a linear model applies and round to the nearest cent.”
Click here to see answer by josgarithmetic(39617) |
Question 1125847: Can anyone help me set this up and solve? I am having some trouble with this conceot. Thank you.
Alvin paddled for 2 hours with a 6-km/h current to reach a campsite. The return trip against the same current took 8 hours. Find the speed of the boat in still water.
Click here to see answer by ikleyn(52786) |
Question 1125849: I keep getting this wrong, can someone please assist me - I will be grateful for your help!
Many graduate schools require applicants to take a certain test. Those taking the test receive three scores: a verbal reasoning score, a quantitative reasoning score, and an analytical writing score. In 2013, the average quantitative reasoning score exceeded the average verbal reasoning score by
1.1 points, and the average verbal reasoning score exceeded the analytical writing score by 145.7 points. The sum of the three average scores was
318.9. What was the average score for each category?
The average verbal reasoning score was_____
The average quantitative reasoning score was_____
The average analytical writing score was_____
Click here to see answer by addingup(3677)  |
Question 1126184: Hello! I was wondering if I can have some help on this question here
Salim wants to download a certain number of his favourite tunes using some money he has saved doing odd jobs. At downloads for U, they charge $1.00 per download. He would need to save $17.00 more than he already has in order to download all he wants.
At a competing site, Music bytes, they only charge $0.80 per download. he would have $5.00 left from his savings of he downloads all he wants. How many downloads does Salim want?
I’m pretty sure this is a problem where you would use y=mx+b such as 17+1.00x=y but I’m not entirely sure, some direction would be nice. Thank you for your time!
Click here to see answer by greenestamps(13200)  |
Question 1126184: Hello! I was wondering if I can have some help on this question here
Salim wants to download a certain number of his favourite tunes using some money he has saved doing odd jobs. At downloads for U, they charge $1.00 per download. He would need to save $17.00 more than he already has in order to download all he wants.
At a competing site, Music bytes, they only charge $0.80 per download. he would have $5.00 left from his savings of he downloads all he wants. How many downloads does Salim want?
I’m pretty sure this is a problem where you would use y=mx+b such as 17+1.00x=y but I’m not entirely sure, some direction would be nice. Thank you for your time!
Click here to see answer by addingup(3677) |
Question 1126918: A business invests $50,000 in equipment to produce a new hand-held video game. Each game costs $18.00 to produce and is sold for $32.75. How many hand-held video games must be sold before the business breaks even?
Click here to see answer by addingup(3677) |
Question 1127088: Find the area of a parallelogram bounded by the y-axis, the line
x = 2, the line f(x) = 2 + 2x, and the line parallel to f(x) passing through
(4, 9).
*I have struggling to figure the solution but keep running into confusion. Here is my work so far, so you can see where I am going wrong*
9=2(4)+2
9=8+b
1=b
2x+1=b
Distance formula:(2-4)^2+ (1-9)^2
4 +64
68
Click here to see answer by jim_thompson5910(35256) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515
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