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 #1Q2 = Quantity produced at Chocolate Factory #2Daily total overall production:Q1 – Q2 = 420At present, each factory produces half the overall requirement. This means thatQ1 = 210, Q2 = 210 a) At present what is the outy produced factory # 01? b) At present the total cost of production of Factory is :TC1(Q) = TC₁(210) = $980.75What is the total cost of production (in dollars) of Factory #2TC2(Q) = TC2(210) = $____________ c) When each factory produces 210 kiograms, the average cost of production in Factory 1 is: AC1(210) = 4.67What is the average cost in Factory 2AC2(210) = $__________ Factory #2 Cost DataFactory #2 has instead the following, different,total daily cost function:TC2(Q2) = P0 · (Q2)² + · (Q2) + 480120In decimal form, the same total cost function ofFactory #2 is:TC2(Q2) = 0.00833 · (Q2)² + 1.075 · (Q2) + 480The marginal cost function of Factory #2 can bederived to be:MC2(Q2) = Q2+4340In decimal form, the same marginal cost functionof Factory #2 is:MC2(Q2) = 0.01667 · Q2 +1.075In all functions, Q represents kilograms ofchocolate produced daily. Factory #1 Cost DataFactory #1 has the following daily total costfunction:TC:(Q1) = (Q1)² + } · (Q1) + 2048In decimal form, the same total cost function is:TC(Q1) = 0.02083 - (Q1)? + 0.2 · (Q1) + 20The marginal cost function of Factory #1 can bederived to be:MC(Q1) = Q1 +248In decimal form, the same marginal cost functionof Factory #1 is:MC1(Q1) = 0.04167 · Q1 +0.2

TC1(Q1) = 0.02083 *Q12 + 0.2 (Q1) - 20 MC1(Q1) = 0.04167*Q1 + 0.2 TC2(Q2) = 0.0083*(Q2)2 +…

Answered: You manage two chocolate factories.…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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

a) At present what is the outy produced factory # 01?

b) At present the total cost of production of Factory is :

TC₁(Q) ₌ TC₁(210) = $980.75

What is the total cost of production (in dollars) of Factory #2

TC₂(Q) = TC₂(210) = $____________

c) When each factory produces 210 kiograms, the average cost of production in Factory 1 is: AC₁(210) = 4.67

What is the average cost in Factory 2

AC₂(210) = $__________

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.

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

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