Question

A toy factory creates miniature steel train engines and box cars. The fabrication department has 4,079 minutes available per week and the assembly and finishing department has 2,999 minutes available per week. Manufacturing one miniature steel train engine requires 10 minutes of fabrication and 5 minutes of assembling and finishing. Manufacturing one miniature steel box car requires 4 minutes of fabrication and 5 minutes of assembling and finishing. The profit on each miniature steel train engine is $5.00 and the profit on each miniature steel box car is $4.25.

Set up a formal linear program that could be used to solve a problem involving this story.
(Use
for box car and
for train engine.)

Answer 1

Answer: The formal linear program can be set up as follows:

Maximize: 5x + 4.25y

Subject to:

10x + 4y <= 4079 (fabrication constraint)

5x + 5y <= 2999 (assembly and finishing constraint)

x >= 0, y >= 0 (non-negativity constraints)

where x is the number of miniature steel train engines and y is the number of miniature steel box cars.

The objective is to maximize the profit, which is represented by the linear function 5x + 4.25y. The fabrication constraint states that the total fabrication time for both products should not exceed 4,079 minutes per week, and the assembly and finishing constraint states that the total assembly and finishing time should not exceed 2,999 minutes per week. The non-negativity constraints ensure that the number of both products is positive.

Explanation: