Near Corporation's two products have the following characteristics: The constrained resource is a particular machine that is available for 10, 400 minutes each month.Each unit of product L06K requires 16 minutes on this machine and each unit of product G57S requires 5 minutes on this machine. How many units of product L06K should be produced each month?
A)975
B)500
C)0
D)175

Question

Near Corporation's two products have the following characteristics:  The constrained resource is a particular machine that is available for 10, 400 minutes each month.Each unit of product L06K requires 16 minutes on this machine and each unit of product G57S requires 5 minutes on this machine. How many units of product L06K should be produced each month?
A)975 
B)500 
C)0 
D)175

Quizplus · Accepted Answer

To maximize the production within the constraints, we can use linear programming. Let x be the number of units of product L06K produced each month, and y be the number of units of product G57S produced each month.

We want to maximize x, subject to the following constraints:

16x + 5y <= 10,400 (constraint on the available machine time)
x >= 0 (non-negativity constraint)

Solving the above constraints, we get:

y <= (10,400 - 16x)/5
y <= 2,080 - 3.2x

To maximize x, we need to minimize y. Therefore, we can choose the highest value of x that satisfies the above constraint:

x = 175 (rounded down from 175.625)

Substituting this value of x in the constraint on y, we get:

y <= 2,080 - 3.2(175) = 520

Therefore, the best choice is to produce 175 units of product L06K each month. This would leave 520 - 5y = 1200 minutes (20 hours) of machine time available for producing product G57S, which can be produced up to a maximum of 240 units (1200/5). However, this is not a relevant value for this question.

Near Corporation's Two Products Have the Following Characteristics: the Constrained