Profit A manufacturer makes two products, toy trucks and toy fire 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 track 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.
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