The Southfork Feed Company makes a feed mix from four ingredients—oats, corn, soybeans, and a vitamin supplement. The company has 300 pounds of oats, 400 pounds of corn, 200 pounds of soybeans, and 100 pounds of vitamin supplement available for the mix.
The company has the following requirements for the mix:
? At least 30% of the mix must be soybeans.
? At least 20% of the mix must be the vitamin supplement.
? The ratio of corn to oats cannot exceed 2 to 1.
? The amount of oats cannot exceed the amount of soybeans.
? The mix must be at least 500 pounds.
A pound of oats costs $0.50; a pound of corn, $1.20; a pound of soybeans, $0.60; and a pound of vitamin supplement, $2.00. The feed company wants to know the number of pounds of each ingredient to put in the mix in order to minimize cost.
Please answer the following questions:
What recipe should the Southfork Feed Company use to minimize cost? (Please, to make sure that Canvas grades your answer correctly, "round up" your answer to the nearest integer and DO NOT use decimals)
Which ingredient(s) the company should not use?
Which of the ingredient constraint(s) is(are) binding?
If they want to invest in procuring extra amounts of one ingredient, which ingredient you recommend they invest in?
If you buy more of this ingredient, what would be the impact on the total cost of the mix?
What is the maximum amount they should be willing to pay for procuring each pound of this ingredient?
If the vendor of Oats increases the per pound price by $0.75, would you recommend the company reduce the use of Oats in making the mix in order to minimize their cost?
If the vendor of Corn reduces the per pound price by $0.75, would you recommend the company increase the use of Corn in making the mix in order to minimize their cost?
If the vendor of Oats offers to supply you Oats for Free(!), would/could you possibly increase the amount of Oats you use to make the mix in order to reduce the cost of the mix?
If the Vitamin becomes ridiculously expensive, would you or could you reduce the use of Vitamin in making the mix?