Profit Maximization
Interstate Bakeries, Inc., is an Atlanta-based manufacturer and dis- tributor of branded bread products. Two leading products, Low Calorie, QA, and High Fiber, QB, bread, are produced using the same baking facility and staff. Low Calorie bread requires 0.3 hours of worker time per case, whereas High Fiber bread requires 0.4 hours of worker time per case. During any given week, a maximum of 15,000 worker hours are available for these two products. To meet grocery retailer demands for a full product line of branded bread prod- ucts, Interstate must produce a minimum of 25,000 cases of Low Calorie bread and 7,500 cases of High Fiber bread per week. Given the popularity of low-calorie products in general, Interstate must also ensure that weekly production of Low Calorie bread is at least twice that of High Fiber bread.
Low Calorie bread is sold to groceries at a price of $42 per case; the price of High Fiber bread is $40 per case. Despite its lower price, the markup on High Fiber bread substantially exceeds that on Low Calorie bread. Variable costs are $30.50 per case for Low Calorie bread, but only $17 per case for High Fiber bread.
A. Set up the linear programming problem that the firm would use to determine the profit- maximizing output levels for Low Calorie and High Fiber bread. Show both the inequal- ity and equality forms of the constraint conditions.
B. Completely solve the linear programming problem.
C. Interpret the solution values for the linear programming problem.
D. Holding all else equal, how much would variable costs per unit on High Fiber bread have to fall before the production level indicated in part B would change?