Question #283245

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.


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
2021-12-28T17:26:37-0500

                  Microcomputer \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Microcomputer }Model 1Model 2Model 3Wholesaleprice/unit$500$1000$1500Materialcost/unit$175$400$750Laborcost/unit$100$150$225\def\arraystretch{1.5} \begin{array}{c:c:c:c} & Model\ 1 & Model\ 2 & Model\ 3 \\ \hline Wholesale\\ price/unit & \$500 & \$1000 & \$1500 \\ \hdashline Material\\ cost/unit & \$175 & \$400 & \$750 \\ \hdashline Labor\\ cost/unit & \$100 & \$150 & \$225 \\ \hdashline \end{array}

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


TR1=500Q1,TR_1 = 500Q_1,

TR2=1000Q2,TR_2 = 1000Q_2,

TR3=1500Q3.TR_3 = 1500Q_3.

An annual total cost functions for manufacturing the three models:


TC1=25000000/3+(175+100)Q1,TC_1 = 25000000/3+(175+100)Q_1,

TC2=25000000/3+(400+150)Q2,TC_2= 25000000/3+(400+150)Q_2,

TC3=25000000/3+(750+225)Q3.TC_3= 25000000/3+(750+225)Q_3.

The profit functions for sales of the three models are:


TP1=TR1TC1TP_1 =TR_1-TC_1

=500Q1(25000000/3+275Q1)= 500Q_1 - (25000000/3 + 275Q_1)

=225Q125000000/3,= 225Q_1 - 25000000/3 ,


TP2=TR2TC2TP_2=TR_2-TC_2

=1000Q2(25000000/3+550Q2)= 1000Q_2 - (25000000/3 + 550Q_2)

=450Q225000000/3,= 450Q_2 - 25000000/3 ,


TP3=TR3TC3TP_3 =TR_3-TC_3

=1500Q3(25000000/3+975Q3)= 1500Q_3 - (25000000/3 + 975Q_3)

=525Q325000000/3.= 525Q_3 - 25000000/3.

If the firm sells 20,000, 40,000 and 10,000 units, respectively of the three models


Q1=20000,Q2=40000,Q3=10000Q_1=20000, Q_2=40000, Q_3=10000

TP=TP1+TP2+TP3TP=TP_1+TP_2+TP_3

=225(20000)25000000/3= 225(20000) - 25000000/3

+450(40000)25000000/3+450(40000) - 25000000/3

+525(10000)25000000/3+525(10000) - 25000000/3

=2750000=2750000

An annual profit if the firm sells 20,000, 40,000 and 10,000 units, respectively of the three models is $2,750,000.



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