Answered: You manage two chocolate factories.…

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter8: Cost Analysis

Section: Chapter Questions

Problem 2.1CE

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Question

You manage two chocolate factories. Using only these two factories, you must produce exactly 420 kgs of chocolate daily at lowest possible cost. Mathematically, you have:

Q₁ = Quantity produced at Chocolate Factory #1

Q₂ = Quantity produced at Chocolate Factory #2

Daily total overall production:

Q₁ – Q₂ = 420

At present, each factory produces half the overall requirement. This means that

Q₁ = 210, Q₂ = 210

Following your logic , you realize that as long as the marginal cost is different between the two factories, you can lower overall cost while maintaining production at 420 kgs.

So, to reduce the overall cost to the lowest possible, you decide to move more than 1 kilogram from one factory to another. As a result, each factory will produce a different quantity of chocolate while the overall daily production remains at 420 kgs. To minimize overall cost, how many kilograms will you order/instruct Factory #1 to produce?

Q_{1 = ____________kgs}

And how many kilograms would you order/instruct Factory #2 to produce?

Q₂= _________kgs

With your new instructions, what is the marginal cost at Factory #1?

MC₁ = $___________

And with your new instructions, what is the marginal cost at Factory #2?

MC₂ = $ ___________

Factory #1 Cost Data
Factory #1 has the following daily total cost
function:
TC:(Q1) = (Q1)² + } · (Q1) + 20
48
In decimal form, the same total cost function is:
TC(Q1) = 0.02083 - (Q1)? + 0.2 · (Q1) + 20
The marginal cost function of Factory #1 can be
derived to be:
MC(Q1) = Q1 +
2
48
In decimal form, the same marginal cost function
of Factory #1 is:
MC1(Q1) = 0.04167 · Q1 +0.2

Factory #2 Cost Data
Factory #2 has instead the following, different,
total daily cost function:
TC2(Q2) = P0 · (Q2)² + · (Q2) + 480
120
In decimal form, the same total cost function of
Factory #2 is:
TC2(Q2) = 0.00833 · (Q2)² + 1.075 · (Q2) + 480
The marginal cost function of Factory #2 can be
derived to be:
MC2(Q2) = Q2+
43
40
In decimal form, the same marginal cost function
of Factory #2 is:
MC2(Q2) = 0.01667 · Q2 +1.075
In all functions, Q represents kilograms of
chocolate produced daily.

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