Question

Hebble Tires produces three types of tires. In their manufacture, the tires are processed on two machines, a molder and a capper. The time (in hours) required on each machine and the income (wholesale selling price less costs, including labor at the regular pay rate) per unit made of each type of tire are: Machine Time (hr) TypeMolderCapper Income($) 45 53 37 4 10 6 Contractual demands for the next month call for the delivery of at least 75 units of each type of tire. To meet these demands while maximizing net income, the company has set aside 3400 hr of machine time at regular pay for the molder and 2700 hr at regular pay for the capper. There is also available up to a total of 1000 hr of overtime that can be divided in any manner and used among the two machines. Overtime pay is $12/hr more than regular-time pay, and this cost must be considered in determining net income. Your task is to determine an operating schedule that maximizes net income.

Answer 1

Let x1, x2, and x3 be the number of Type 1, 2, and 3 tires to be produced. Also, let T1, T2, and T be the Molder, Capper, and Total overtime hours to be made.

Maximize 45 x1 + 53 x2 + 37 x3 - 12 T

Subject to,

8 x1 + 10 x2 + 5 x3 - T1 <= 3400

4 x1 + 7 x2 + 6 x3 - t2 <= 2700

T1 + T2 = T

T <= 1000

x1 >= 75

x2 >= 75

x3 >= 75

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LINDO Code

Max 45 x1 + 53 x2 + 37 x3 - 12 T
s.t.
8 x1 + 10 x2 + 5 x3 - T1 <= 3400
4 x1 + 7 x2 + 6 x3 - t2 <= 2700
T1 + T2 - T = 0
T <= 1000
x1 >= 75
x2 >= 75
x3 >= 75
end

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Solution

Global optimal solution found. Objective value: Infeasibilities: Total solver iterations Elapsed runtime seconds: 21036.61 0.000000 0.43 Model Class: LP Total variables: Nonlinear variables: Integer variables: Total constraints: Nonlinear constraints: 19 Total nonzeros Nonlinear nonzeros Variable X1 X2 X3 Value 179.4643 75.00000 242.8571 0.000000 0.000000 0.000000 Tl T2