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.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
Please DO NOT POST MORE THAN ONE PROBLEM per post.
It is the rule, the policy and the requirement of this forum.
Thank you very much for your cooperation.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! 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.
Problems WITH YOUR POST:
1) TOO MANY PROBLEMS
2) PROBLEMS ARE BORING TO READ
3) PROBLEMS ARE TOO LONG
4) READING THE PROBLEMS IS VERY TIME-CONSUMING
5) DOING THE PROBLEMS ACCURATELY AND CONCISELY WILL TAKE A LOT OF EFFORT
6) I WONDER IF THE WORD "PLEASE" IS A PART OF YOUR VOCABULARY
Therefore, you must do it on your own or find someone who'll take the time to do it for you. Maybe someone here will, but DEFINITELY NOT I!
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