Problem:
Mallory Furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. This problem was formulated as a linear programming problem, and the solution was obtained using a computer software package. At the optimal solution point, the maximum profit is $45,000. In order to obtain the maximum profit, Mallory Furniture should purchase 150 big shelves and no medium shelves. The sensitivity range for the profit of the big shelf is from 250 to . The sensitivity range for the profit of the medium shelf is from to 180. If the Mallory Furniture is able to increase the profit per medium shelf to $200, would the company purchase medium shelves. What would be the new product mix and the total profit?