Question

3 Question 2. Hart Manufacturing makes 3 products. Each product requires manufacturing operations in three departments: A, B, C. The labor requirements (in hour), by department, are as follows: Department Product 1 Product 2 Product 3 A 2 B 2.5 с 0.25 During the next production period the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3. Develop an all-integer optimization model to determine the production quantity for each product that maximizes the total profit contribution. (Do NOT solve the model.) (15 points) 1.5 2 0.25 1 0.25

Answer 1

Let,

x1 = number of product 1 to produce
x2 = number of product 2 to produce
x3 = number of product 3 to produce

objective is to maximize profit = Max 25x1+28x2+30x3

subject to,

1.5x1+3x2+2x3 <= 450 (Department A)
2x1+1x2+2.5x3 <= 350 (Department B)
0.25x1+0.25x2+0.25x3 <= 50 (Department C)

x1,x2,x3 = integer and x1,x2,x3 >= 0