The Pacific Computer Company Makes Two Models of Notebook PersonalManufacturing Time Available in Department a for the Coming Week

Question

Examlex · Accepted Answer

The Answer is a. The objective function for maximizing profit is max Z = 100x₁ + 150 x₂.x₁ = Model 410 units produced; x₂ = Model 540 units produced
Max z = 100 x₁ + 150 x₂
subject to: 5x₁ + 10 x₂

\le

300 (Dept. A)
14x₁ + 7x₂

\le

420 (Dept. B)
25x₁ + 40x₂

\ge

1600 (Assembly)
b. Since the manufacturing time is 300 minutes, the constraint corresponding to Department
A, assuming x₁ corresponds to Model 410 is 5x₁ + 10x₂

\le

300.
c. The optimum solution point is x₁ = 20; x₂ = 20.x₁ = 0 and 5x₁+ 10 x₂= 300
=> 5(0) + 10x₁= 300 => x₂= 30 => (0, 30)
5x₁ + 10x₂= 300 and 14x₂+ 7x₂ = 420
=> 21 x₂ = 420 => x₂ = 20 and x₁= 20 => (20, 20)
14 x₁ + 7x₂ = 420 and x₂= 0
=> 14 x₁ + 7(0) = 420 => x₁ = 30 => (30, 0)
x₁ = 0 and x₂ = 0 => (0, 0)
d. The maximum possible total profit is $5000.Maximum profit = 100 x₁ + 150 x₂
100(0) + 150 (30) = 4,500
100(20) + 150(20) = 5,000-- optimum
100(30) + 150(0) = 3,000
100(0) + 150(0) = 0

The Pacific Computer Company Makes Two Models of Notebook Personal

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