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# Finite Mathematics - Method of Surplus Variables and Duals

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A store sells two brands of snacks. A package of Sun Hill costs \$3 and contains 10 oz of peanuts, 4 oz of raisins, and 2 oz of rolled oats. A package of Bear Valley costs \$2 and contains 2 oz of peanuts, 4 oz of raisins, and 8 oz of rolled oats. Suppose you wish to make a mixture that contains at least 20 oz of peanuts, 24 oz of raisins, and 24 oz of rolled oats.

We may use an applet or something from the internet to help, but please explain each step.

a. Using the method of surplus variables, find how many packages of each you should buy to minimize the cost. What is the minimum cost?

b. Using the method of duals, find how many packages of each you should buy to minimize the cost. What is the minimum cost?

c. Suppose the minimum amount of peanuts is increased to 28. Use shadow costs to calculate the total cost in this case.

d. Explain why it makes sense that the shadow cost for the rolled oats is 0.