4. M5 Manufacturing creates breakdown beds for a major retailer. They have a del

Question

4. M5 Manufacturing creates breakdown beds for a major retailer. They have a deluxe bed with built-in shelving that sells for $500. They also have a standard headboard that sells for $300. Finally, they sell a very simple frame that costs $200. The manufacturing process breaks down into three steps. The company has 3000 labor hours for primary production, 1300 labor hours for assembly prep, and 800 labor hours for shipping. The breakdown of how long each bed requires in each departm ent looks like this Shipping Deluxe Standard Frame Primary Production Assembly Prep 3.5 2.0 Given the time constraints, how many of each bed should the company produce to maximize profits?

Explanation / Answer

Variables - Delux, Standard and Frames are D, S and F

Constraints -

1. D, S and F are non-negative integers

2. 3.5D+2S+F <= 3000

3. 1.5D+S+0.5F <= 1500

4. D+0.5S+0.5F <= 800

Objective

Maximize the revenue 500D+300S+200F

(note that profits are not given)

solution

deluxe = 0

Standard = 1400

Frames = 200

per model Total Model Optimal primary assemble shipping revenue primary assemble shipping revenue Deluxe 0 3.5 1.5 1 500 0 0 0 0 Standard 1400 2 1 0.5 300 2800 1400 700 420000 Frame 200 1 0.5 0.5 200 200 100 100 40000 Total 3000 1500 800 460000 Max possible 3000 1300 800 Constraint 0 0 0

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