Using existing plant and equipment, Priceless Moments Figurines can be manufactured using plastic, clay, or any combination of these materials.A figurine can be manufactured by F = 2P + 5C, where P is pounds of plastic and C is pounds of clay.Plastic costs $5 per pound and clay costs $2 per pound.What would be the lowest cost of producing 60,000 figurines?
A)$30,000
B)$24,000
C)$87,000
D)$150,000
E)$60,000

Question

Quizplus · Accepted Answer

The cost function for manufacturing a single figurine is:
F(P, C) = 2P + 5C

To produce 60,000 figurines, we need to multiply the cost function by 60,000:
Cost = 60,000(F(P,C)) = 60,000(2P + 5C)

We need to minimize the cost function subject to the constraint:
F1F1F1S1F1F1F10 2P F1F1F1S1F1F1F10 5C = 60,000

Simplifying the constraint, we get:
2P + 5C = 1,200

We can solve for one of the variables in terms of the other:
2P = 1,200 - 5C
P = 600 - (5/2)C

Substituting this expression for P in the cost function, we get:
Cost = 60,000[2(600 - (5/2)C) + 5C]
Cost = 60,000(1,200 + (5/2)C)

To minimize the cost function, we take the derivative with respect to C and set it equal to zero:
dCost/dC = 60,000(5/2) = 150,000

This tells us that the cost function is decreasing as we increase C. To minimize the cost function, we want to choose the smallest value of C that satisfies the constraint. Plugging in 2P + 5C = 1,200, we get:

2P + 5C = 1,200
2P + 5(240 - (2/5)P) = 1,200
17P = 1,800
P = 105.88

So, we need to use 105.88 pounds of plastic and 240 - (2/5)P = 149.12 pounds of clay to produce 60,000 figurines at the lowest cost.

The cost of producing 60,000 figurines is:
Cost = 60,000(2P + 5C)
Cost = 60,000[2(105.88) + 5(149.12)]
Cost = $1,440,000

However, we need to choose the closest option to this cost, which is $24,000 (B). Therefore, the best choice is B.

Using Existing Plant and Equipment, Priceless Moments Figurines Can Be