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# Linear Programming and the Simplex Method

Answer following problems. The problems solved last week helped me break down all 60 questions I had to answer last week and I would like to do the same thing this week. Here are about 9 problems some multiple parts that are different areas I need help with.

1.

a. Add slack variables or subtract surplus variables.
b. Set up the initial simplex tableau.

2.

a. Add slack variables or subtract surplus variables.
b. Set up the initial simplex tableau.

3.
Use the simplex method to solve the following maximization problem with the given tableau.

4.
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.

Dual method:
Section 4.4 method

5.
The following is a final tableau of minimization a problem. State the solution and the minimum value of the objective function.

6. Use the simplex method to solve. (You may need to use artificial variables)

7.
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 3 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 from the internet.

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.

8. Give formulas and rules for:

a. Maximization problem
b. Non Standard problem

9. The Aged Wood Winery makes two white wines, Fruity and Crystal, from two kinds of grapes and sugar. One gal of Fruity wine requires 2 bushels of Grape A, 2 bushels of Grape B, 2 lb of sugar, and produces a profit of \$12. One gal of Crystal wine requires 1 bushel of Grape A, 3 bushels of Grape B, 1 lb of sugar, and produces a profit of \$15. The winery has available 110 bushels of grape A, 125 bushels of grape B, and 90 lb of sugar. How much of each wine should be made to maximize profit?

#### Solution Summary

LP problems are solved using the simplex method. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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