Answer to Question #127969 in Math for Sheraz

Question #127969
A manufacturer of microcomputer produces three different models. The following table summarizes wholesale process, material cost per unit and labor cost per unit. Annual fixed costs are $ 25 million.

Microcomputer


Model 1
Model 2
Model 3

Wholesale price per unit
$500
$1,000
$1,500

Material cost per unit
$175
$400
$750

Labor cost per unit
$100
$150
$225

Determine a joint total revenue function for sale of the three different microcomputer models?
Determine an annual total cost function for manufacturing the three models.
Determine the profit function for sales of the three models.
What is an annual profit if the firm sells 20,000, 40,000 and 10,000 units, respectively of the three models?
1
Expert's answer
2020-08-03T16:21:14-0400

A joint total revenue functions for sale of the three different microcomputer models are:

TR1 = 500*Q1,

TR2 = 1,000*Q2,

TR3 = 1,500*Q3.

An annual total cost functions for manufacturing the three models:

TC1 = 25,000,000/3 + 275Q1,

TC2 = 25,000,000/3 + 550Q2,

TC3 = 25,000,000/3 + 975Q3.

The profit functions for sales of the three models are:

TP1 = 500Q1 - (25,000,000/3 + 275Q1) = 225Q1 - 25,000,000/3,

TP2 = 1,000Q2 - (25,000,000/3 + 550Q2) = 450Q2 - 25,000,000/3,

TP3 = 1,500Q3 - (25,000,000/3 + 975Q3) = 525Q3 - 25,000,000/3.

TP = 225*20,000 + 450*40,000 + 525*10,000 - 25,000,000 = 2,750,000.


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Comments

Assignment Expert
23.11.20, 00:44

The value of Q1 was not given in the question. One should substitute the corresponding value for Q1 into TR1=500*Q1 if one knows it. If we do not know it exactly, then it was denoted by the unknown variable Q1. Next, $500-$275=$225, $1000-$550=$450 according to formulas of TP1, TP2. The value $975=$750+$225 is the sum of material cost per unit and labor cost per unit for Model 3 using initial conditions of the question.

Assignment Expert
22.11.20, 12:19

Customer (maan.chohan@gmail.com): Im facing a problem with the q1, q2, q3 values like IN TR1 = 500*Q1, What value will we take? secondly where does 225, 450, 975 values came from ?

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