The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X1 = number of product 1 produced in each batch X2 = number of product 2 produced in each batch MAX: 150 X1 + 250 X2 Subject to: 2 X1 + 5 X2 ≤ 200 3 X1 + 7 X2 ≤ 175 X1, X2 ≥ 0 Solve for how many units of resource two (the second constraint) are unutilized if the company produces 10 units of product 1 and 5 units of product 2?
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The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X1 = number of product 1 produced in each batch X2 = number of product 2 produced in each batch MAX: 150 X1 + 250 X2 Subject to: 2X1 + 5 X2 ≤ 200 3X1 + 7 X2 ≤ 175 X1, X2 ≥ 0 How much profit is earned per each unit of product 2 produced? a. 150 b. 175 c. 200 d. 250
Rachel G.
The following linear programming problem maximizes profits by producing two products. Z1 = number of units of product 1 produced in each batch Z2 = number of units of product 2 produced in each batch Maximize: 1750 Z1 + 2100 Z2 Subject to: 2 Z1 + 5 Z2 ≤ 200 (Resource 1) 3 Z1 + 7 Z2 ≤ 175 (Resource 2) 4 Z1 + 5 Z2 ≤ 275 (Resource 3) Z1, Z2 ≥ 0 How much profit is earned per unit of product 2 produced? a. 1750 b. 2100 c. 3850 d. None of the above
Lucas F.
A company produces two products, A and B. The sales volume for A is at least 80% of the total sales of both A and B. However, the company cannot sell more than 110 units of A per day. Both products use one raw material, of which the maximum daily availability is 300 lb. The usage rates of the raw material are 2 lb per unit of A, and 4 lb per unit of B. The profit for units of A and B are Rs.400 and Rs.900, respectively. Determine the optimal product mix for the company. i. Formulate the problem in terms of a Linear Programming model. ii. Determine the optimal mix of the two products by graphical method.
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