Question

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?

Answer 1

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.