27 The following question concerns the Rylon example discussed in Section 3.9. After defining RB = ounces of Regular Brute produced annually LB=  ounces of Luxury Brute produced annually RC = ounces of Regular Chanelle produced annually LC  =ounces of Luxury Chanelle produced annually RM = pounds of raw material purchased annually the LINDO output in Figure 15 was obtained for this problem.

Use this output to answer the following questions:

a Interpret the shadow price of each constraint.

b If the price of RB were to increase by 50¢, what would be the new optimal solution to the Rylon problem?

c If 8,000 laboratory hours were available each year, but only 2,000 lb of raw material were available each year, would Rylon’s profits increase or decrease? [Hint:

Use the 100% Rule to show that the current basis remains optimal. Then use reasoning analogous to

(34)–(37) to determine the new objective function value.]

d Rylon is considering expanding its laboratory capacity.

Two options are under consideration:

Option 1 For a cost of $10,000 (incurred now), annual laboratory capacity can be increased by 1,000 hours.

Option 2 For a cost of $200,000 (incurred now), annual laboratory capacity can be increased by 10,000 hours.

Suppose that all other aspects of the problem remain unchanged and that future profits are discounted, with the interest rate being 11

1 9

% per year. Which option, if any, should Rylon choose?

e Rylon is considering purchasing a new type of raw material. Unlimited quantities can be purchased at $8/lb.

It requires 3 laboratory hours to process a pound of the new raw material. Each processed pound yields 2 oz of RB and 1 oz of RC. Should Rylon purchase any of the new material?