The Hansel Corporation, located in Bangalore, India, makes plastics materials that are mixed with various additives and reinforcing materials before being melted, extruded, and cut into small pellets for sale to other manufacturers. Four grades of plastic are made, each of which might include up to four different additives. The following table shows the number of pounds of additive per pound of each grade of final product, the weekly availability of the additives, and cost and profitability information.

Grade 1 Grade 2 Grade 3 Grade 4 Availability Additive A 0.40 0.37 0.34 0.90 100,000 Additive B 0.30 0.33 0.33 90,000 Additive C 0.20 0.25 0.33 40,000 Additive D 0.10 0.05 0.10 10,000 Profit/lb $2.00 $1.70 $1.50 $2.80 Because of marketing considerations, the total amount of grades 1 and 2 should not exceed 65% of the total of all grades produced, and at least 25% of the total product mix should be grade 4.

a. How much of each grade should be produced to maximize profit? Develop and solve a linear optimization model.

b. A labor strike in India leads to a shortage of 20,000 units of additive C. What should the production manager do?

c. Management is considering raising the price on grade 2 to $2.00 per pound. How will the solution be changed?