Chapter 4.2, Problem 30E

Profit A manufacturer makes two products, toy trucks and toy fine engines. Both are processed in four different departments, each of which has a limited capacity. The sheet metal department requires 2 hours for each truck and 3 hours for each fire engine and has a total of 24,000 hours available. The truck assembly department can handle at most 6600 trucks per week; and the fire engine assembly department assembles at most 5500 fire engines weekly. The painting department, which finishes both toys, has a maximum capacity of 10,000 per week,

(a) If the profit is $8.50 for a toy truck and $12.10 for a toy fire engine, how many of each item should the company produce to maximize profit?

(b) Keeping the profit for a toy truck at $8.50, use the graphical method to find the largest possible profit less than $12.10 for a toy fire engine that would result in an additional solution besides the one found in part (a). What is the additional solution? Verify this solution using the simplex method.

(c) Keeping the profit for a toy truck at $8.50, use the graphical method to find the smallest possible profit greater than $12.10 for a toy fire engine that would result in an additional solution besides the one found in part (a). What is the additional solution? Verify this solution using the simplex method.