Question

A tailor makes wool tweed sport coats and wool slacks. He is able to get a shipment of 150 square yards of wool cloth from Scotland each month to make coats and slacks, and he has 200 hours of his own labor to make them each month. A coat requires 3 square yards of wool and 10 hours to make, and a pair of slacks requires 5 square yards of wool and 4 hours to make. The tailor earns $50 in profit from each coat he makes and $40 from each pair of slacks. He wants to know how many coats and pairs of slacks to produce to maximize profit. Formulate an integer linear programming model for this problem. Determine the integer solution to this problem by using branch bound Method.

Answer 1

To solve this problem using integer linear programming, let's define the decision variables and set up the objective function and constraints. Using the branch and bound method, we can find the integer solution that maximizes profit.

Step-by-step explanation:

To solve this problem using integer linear programming, let's define the decision variables:

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• x = number of coats to produce
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• y = number of slacks to produce

The objective function is to maximize profit, which can be expressed as:

Profit = 50x + 40y

Now, let's use the constraints:

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• 3x + 5y ≤ 150 (constraint on wool)
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• 10x + 4y ≤ 200 (constraint on labor)
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• x, y ≥ 0 (non-negativity constraint)

Using branch and bound method, we can solve this problem by dividing the feasible region into smaller subregions and exploring them.

By analyzing the constraints and objective function, we can find the integer solution that maximizes profit.