Question

At a chip manufacturing plant, four technicians (A, B, C, and D) produce three products (Products 1, 2, and 3). This month, the chip manufacturer can sell 80 units of Product 1, 50 units of Product 2, and at most 50 units of Product 3. Technician A can make only Products 1 and 3. Technician B can make only Products 1 and 2. Technician C can make only Product 3. Technician D can make only Product 2. For each unit produced, the products contribute the following profit: Product 1, $6; Product 2, $7; and Product 3, $10. The time (in hours) each technician needs to manufacture a product is as follows(X means the technician can not produce the corresponding product). Each technician can work up to 120 hours per month. How can the chip manufacturer maximize its montly profit

Answer 1

The chip manufacturer can maximize the monthly profit by using the objective function: z = 6X₁ + 7X₂ + 10 X₃

An objective function is a function that has the goal of maximizing or minimizing the model's value based on the relationship between the variables in the function.

The term "decision variables" refers to a group of variables that are responsible for regulating the objective function.

The decision variable for the quantity of the product 1, 2, 3 manufactured can be expressed as:

• X₁, X₂, X₃

The objective function used in maximizing the profit is:

• z = 6X₁ + 7X₂ + 10 X₃

This is subjected to the constraint:

• 2X₁ + 3X₃  ≤  120     (Tech A time and manufacturing limitation)
• 2.5X₁ + 3X₂  ≤  120  (Tech B time and manufacturing limitation)
• 4X₂  ≤  120               (Tech C time and manufacturing limitation)
• 3.5X₂  ≤  120            (Tech D time and manufacturing limitation)

Learn more about objective function for maximizing profit here:

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