1. As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models; the Deluxe and the Special. The profit on the Deluxe model is $12 per unit and the Special's profit is $10. Each model goes through two phases of the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at eh finishing and inspection time. Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time. The company has also decided that the Special must comprise at least 40 percent of the production total.
a. Formulate this as a linear programming problem.
b. Find the solution that gives the maximum profit.
2. A fabric firm has received an order for cloth specified to contain at least 45 pounds of cotton and 25 pounds of silk. The cloth can be woven out on any suitable mix of two yarns, A and B, Material A cost $3 per pound, and B costs $2 per pound. They contain the following proportions of cotton silk (by weight):
Yarn Cotton: Silk (%)
A 30 50
B 60 10____
What quantities (pounds) of A and B yarns should be used to minimize the cost of this order?