Microcomputer Wholesaleprice/unitMaterialcost/unitLaborcost/unitModel 1$500$175$100Model 2$1000$400$150Model 3$1500$750$225A joint total revenue functions for sale of the three different microcomputer models are:
TR1=500Q1,
TR2=1000Q2,
TR3=1500Q3.
An annual total cost functions for manufacturing the three models:
TC1=25000000/3+(175+100)Q1,
TC2=25000000/3+(400+150)Q2,
TC3=25000000/3+(750+225)Q3.
The profit functions for sales of the three models are:
TP1=TR1−TC1
=500Q1−(25000000/3+275Q1)
=225Q1−25000000/3,
TP2=TR2−TC2
=1000Q2−(25000000/3+550Q2)
=450Q2−25000000/3,
TP3=TR3−TC3
=1500Q3−(25000000/3+975Q3)
=525Q3−25000000/3.If the firm sells 20,000, 40,000 and 10,000 units, respectively of the three models
Q1=20000,Q2=40000,Q3=10000
TP=TP1+TP2+TP3
=225(20000)−25000000/3
+450(40000)−25000000/3
+525(10000)−25000000/3
=2750000An 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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