# Linear Programming

Please see the attached file for the fully formatted problems.

a. Add slack variables or subtract surplus variables.

b. Set up the initial simplex tableau.

a. Add slack variables or subtract surplus variables.

b. Set up the initial simplex tableau.

Use the simplex method to solve the following maximization problem with the given tableau. You may use an applet or something from the internet to help you, but you must explain each step. If you have it worked without an explanation for each step, you will receive no credit.

Convert into a maximization problem and then solve each problem using both the dual method and the method of section 4.4. You may use an applet or something from the internet to help you, but you must explain each step. If you have it worked without an explanation for each step, you will receive no credit.

Dual method:

The following is a final tableau of minimization a problem. State the solution and the minimum value of the objective function.

Use the simplex method to solve. (You may need to use artificial variables) You may use an applet or something from the internet to help you, but you must explain each step. If you have it worked without an explanation for each step, you will receive no credit.

Food Cost 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.

You may use an applet or something from the internet to help you, but you must explain each step. If you have it worked without an explanation for each step, you will receive no credit.

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.

#### Solution Summary

This solution explains the concept of slack variable, surplus variable and simplex method for solving linear programming problems.