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Heniser Pet Foods manufactures two products. X and Y. The unit contribution margins for Products X and Y are US $30 and US $50, respectively. Each product uses Materials A and B. Product X uses 6 pounds of Material A and 12 pounds of Material B. Product Y uses 12 pounds of Material A and 8 pounds of Material B. The company can purchase only 1,200 pounds of Material A and 1,760 pounds of Material B. The optimal mix of products to manufacture is:
A. 146 units of X and 0 units of Y.
B. 0 units of X and 100 units of Y.
C. 120 units of X and 40 units of Y.
D. 40 units of X and 120 units of Y.
Correct Answer: C
Explanation/Reference:
Explanation:
Linear programming is a technique used to maximize a contribution margin function or to minimize a cost function, subject to constraints such as scarce resources or minimum/maximum levels of production. Thus, linear programming is often used for planning resource allocations. In this problem, the equation to be maximized, called the objective function, is: US $30X + $50Y. This equation is to be maximized subject to the constraints on materials.
The two constraint functions are:
Material A: 6X+12Y1.200
Material B: 12X + 8Y 1,760
One way to solve this problem is to graph the constraint lines and determine the feasible area. The optimal production level is at an extreme point within the feasible area. The graph shows that a production level of 120 units of X and 40 units of Y is a feasible production level that maximizes the contribution margin.
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