Tutors Answer Your Questions about Linear-systems (FREE)
Question 1205963: Choosing a phone plan in a college dormitory, each student has a choice of two phone companies. Company A charges $7.46 per month plus 13 cents a call and Company B charges $6.17 per month plus 17 cents per call.
a. About how many phone calls do you make per month?
b. For each company, write an equation which represents the cost in a given month in terms of the number of phone calls.
c. Graph each equation you wrote in part (b). Be sure to label your graph.
d. When are the costs for both companies the same? When is Company A a better choice? When is Company B a better choice?
e. Decide which plan is best for which type of user. Why?
Click here to see answer by josgarithmetic(39617)  |
Question 1206085: Phil’s age is 7 years more than 1/5 times Peter’s age. Also, 4 times Phil’s age is 2 years less than twice Peter’s age. If x is Peter’s age in years, identify the equation that represents this situation and identify the solution to the equation.
Click here to see answer by josgarithmetic(39617) |
Question 1206085: Phil’s age is 7 years more than 1/5 times Peter’s age. Also, 4 times Phil’s age is 2 years less than twice Peter’s age. If x is Peter’s age in years, identify the equation that represents this situation and identify the solution to the equation.
Click here to see answer by MathTherapy(10552)  |
Question 1107560: Bridget's classroom started out with a collection of only 6 books, but she plans to purchase an additional 3 books per week. Cole's library started out with 38 books, and he will purchase another 1 book per week. At what week and amount of books will the two libraries be the same?
Click here to see answer by mananth(16946)  |
Question 1107560: Bridget's classroom started out with a collection of only 6 books, but she plans to purchase an additional 3 books per week. Cole's library started out with 38 books, and he will purchase another 1 book per week. At what week and amount of books will the two libraries be the same?
Click here to see answer by mccravyedwin(407)  |
Question 1107560: Bridget's classroom started out with a collection of only 6 books, but she plans to purchase an additional 3 books per week. Cole's library started out with 38 books, and he will purchase another 1 book per week. At what week and amount of books will the two libraries be the same?
Click here to see answer by ikleyn(52786)  |
Question 1206214: The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and
1
2
hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 24 per day, and the maximum number of painting hours available is 8 per day. If the profit on the deluxe model is $96 per unit and the profit on the economy model is $74 per unit, how many units of each model will maximize profit?
______ deluxe units
______ economy units
Click here to see answer by Theo(13342)  |
Question 1206214: The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and
1
2
hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 24 per day, and the maximum number of painting hours available is 8 per day. If the profit on the deluxe model is $96 per unit and the profit on the economy model is $74 per unit, how many units of each model will maximize profit?
______ deluxe units
______ economy units
Click here to see answer by ikleyn(52786) |
Question 1103529: The Chicago Bulls� arena is called the United Center and the Dallas Mavericks� arena is called the
American Airlines Center. They have a combined capacity of 42,700 people. Five times the
capacity of the American Airlines Center is 2,000 more than four times the capacity of the United
Center. What is the capacity of each arena?
Click here to see answer by mananth(16946) |
Question 1206298: A box company makes small and large wooden boxes. Small boxes require 0,8 square metres of wood, while large ones require 1,4 square metres. All boxes require 0,5 hours of labour, regardless of size. Wood is limited to 42 square metres, and only 24 hours of labour are available. Due to warehouse space limitations, no more than 20 large boxes can be made each day. Also, demand by customers for small boxes is limited to a maximum of 30 boxes. Each small box yields a profit of R42,00 and each large box earns only R14,00.
Formulate a linear programming model for the company as follows;
(1) Clearly identify the two decision variables in respect of each product to be produced.
Let x1 = _____________________________________________________
Let x2 = _____________________________________________________
PAGE 4
(2) Write down the objective function that maximizes total profit.
Maximize z = ________________________________________________
(3) Formulate the constraints in respect of the two resources used in producing the bowls and mugs, warehouse space limitation, and demand limitation.
______________________________________________ m2 of wood
______________________________________________ labour hours
______________________________________________ warehouse
______________________________________________ demand
(4) Indicate that all constraints are non-negative.
x1 ≥ 0 or x1, x2 ≥ 0
x2 ≥ 0
Click here to see answer by Theo(13342) |
Question 1206298: A box company makes small and large wooden boxes. Small boxes require 0,8 square metres of wood, while large ones require 1,4 square metres. All boxes require 0,5 hours of labour, regardless of size. Wood is limited to 42 square metres, and only 24 hours of labour are available. Due to warehouse space limitations, no more than 20 large boxes can be made each day. Also, demand by customers for small boxes is limited to a maximum of 30 boxes. Each small box yields a profit of R42,00 and each large box earns only R14,00.
Formulate a linear programming model for the company as follows;
(1) Clearly identify the two decision variables in respect of each product to be produced.
Let x1 = _____________________________________________________
Let x2 = _____________________________________________________
PAGE 4
(2) Write down the objective function that maximizes total profit.
Maximize z = ________________________________________________
(3) Formulate the constraints in respect of the two resources used in producing the bowls and mugs, warehouse space limitation, and demand limitation.
______________________________________________ m2 of wood
______________________________________________ labour hours
______________________________________________ warehouse
______________________________________________ demand
(4) Indicate that all constraints are non-negative.
x1 ≥ 0 or x1, x2 ≥ 0
x2 ≥ 0
Click here to see answer by ikleyn(52786) |
Question 1207906: A manufacturer makes 2-minute, 6-minute, and 9-minute film developers. Each ton of 2-minute developer requires 6 minutes in plant A and 24 mmutes in plant B. Each ton of 6-minute developer requires 12 minutes in plant A and 12 minutes in plant B. Each ton of 9-minute developer requires 12 minutes in plant A and 12
minutes in plant B. If plant A is available 10 hours per day and plant B is available 16 per day,how many tons of each type of developer can be produced so that the plants are fully used
Click here to see answer by ikleyn(52786) |
Question 1208206: Formulate but do not solve the problem.
A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table.
Sleeveless Short-sleeve Long-sleeve
Cutting 8 12 14
Sewing 22 23 28
Packaging 5 8 8
The cutting, sewing, and packaging departments have available a maximum of 80, 160, and 48 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity? (Let x, y, and z denote the amount of sleeveless, short-sleeve, and long-sleeve, respectively.)
Click here to see answer by ikleyn(52786) |
Question 1208482: 2 Using Desmos :
Luke is starting a landscaping business and will cut lawns. His startup cost to purchase two lawn mowers is $450. He will use $1 in gas for each lawn and will charge $10 per lawn.
a) Write a linear system to represent this problem. Remember to define your variables
Click here to see answer by josgarithmetic(39617) |
Question 1208482: 2 Using Desmos :
Luke is starting a landscaping business and will cut lawns. His startup cost to purchase two lawn mowers is $450. He will use $1 in gas for each lawn and will charge $10 per lawn.
a) Write a linear system to represent this problem. Remember to define your variables
Click here to see answer by MathTherapy(10552) |
Question 1208741: A factory manufactures two types of gadgets, regular and premium. Each gadget requires the use of two operations, assembly and finishing, and there are at most 12 hours available for each operation. A regular gadget requires 1 hour of assembly and 3 hours of finishing, while a premium gadget needs 4 hours of assembly and 5 hour of finishing. Due to other restrictions, the company can make at most 100 gadgets a day. If a profit of $20 is realized for each regular gadget and $30 for a premium gadget, how many of each should be manufactured to maximize profit?
Click here to see answer by math_tutor2020(3817) |
Question 1208741: A factory manufactures two types of gadgets, regular and premium. Each gadget requires the use of two operations, assembly and finishing, and there are at most 12 hours available for each operation. A regular gadget requires 1 hour of assembly and 3 hours of finishing, while a premium gadget needs 4 hours of assembly and 5 hour of finishing. Due to other restrictions, the company can make at most 100 gadgets a day. If a profit of $20 is realized for each regular gadget and $30 for a premium gadget, how many of each should be manufactured to maximize profit?
Click here to see answer by ikleyn(52786) |
Question 1208885: Cannon wants to put as much as he can into an account as soon as he starts working
He deposits 25000 at the end of each year for 5 years in an account paying 6% compounded annually. How much will he have at the end of the 6th year.
Click here to see answer by KMST(5328)  |
Question 1208885: Cannon wants to put as much as he can into an account as soon as he starts working
He deposits 25000 at the end of each year for 5 years in an account paying 6% compounded annually. How much will he have at the end of the 6th year.
Click here to see answer by ikleyn(52786) |
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