Question

A company manufactures two types of cell phones, a basic model and a pro model. The basic model generates a profit of $100 per phone and the pro model has a profit of $150 per phone. On the assembly line the basic phone requires 7 hours, while the pro model takes 11 hours. The basic phone requires 1 hour and the pro phone needs 3 hours for finishing, which includes loading software. Both phones require 1 hour for testing. On a particular production run the company has available 1,540 work hours on the assembly line, 360 work hours for finishing, and 200 work hours in the testing department. What is that maximum profit from manufacturing both phones? Round your answer to the nearest whole number. Do not include a dollar sign or comma in your answer.

Answer 1

Answer

Units of basic model = 165

Units of pro model = 35

Calculations:

Let units of basic model be x.

Let units of pro model be y.

Profit Function that needs to be maximized = 100x + 150y

Given that:

7x + 11y < 1540

x + 3y < 360

x + y < 200

x > 0

y >0

Plotting it on a graph, we get-

X+YS 200 (0.120) (68.99) (165,35) x+3y< 360 (2000) 300 K 7x+ly $1540

(0.120) P= 0 + 120-150 = 18000 → (66,98) P=100.66 +98.150 = 6600 + 14700 21300 → (165,35) P= 100.165 + 150.35 = 16500 + 5250 = [21750 Maximum Profit will achieve → (200,0) - in producing 165 Basis model P= 100-200 + 150.0 = 20000 C and 35 Pro models.

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