SOLUTION: A Manufacturer of microcomputers produces three different models as shown in Table 2. The following summarizes wholesale prices, material cost per unit, and labor cost per unit.Ann

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Question 1164636: A Manufacturer of microcomputers produces three different models as shown in Table 2. The following summarizes wholesale prices, material cost per unit, and labor cost per unit.Annual fixed cost are $25 million.


Model 1 Model 2 Model 3
Wholesale price/unit 500 1000 1500
Material Cost / unit 175 400 750
Labor cost / unit 100 150 225

Required:
i. Determine a joint revenue function for sales of the three different microcomputer models
ii. Determine the annual costs function for the manufacturing the three models.
iii. Determine the profit function for sales of the three models?

Answer by ikleyn(53618) About Me  (Show Source):
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A Manufacturer of microcomputers produces three different models as shown in Table 2.
The following summarizes wholesale prices, material cost per unit, and labor cost per unit.
Annual fixed cost are $25 million. 
                      Model 1  Model 2  Model 3

Wholesale price/unit   $500     $1000    $1500
Material Cost / unit   $175      $400     $750
Labor cost / unit      $100      $150     $225

i. Determine a joint revenue function for sales of the three different microcomputer models
ii. Determine the annual costs function for the manufacturing the three models.
iii. Determine the profit function for sales of the three models?
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(i)  The joint revenue function is the function of three arguments (n1,n2,n3), 
     where n1 is the number of units of Model 1, n2 is the number of units of Model 2, 
     and   n3 is the number of units of Model 3 produced per year.


     The joint revenue function is

        R(n1,n2,n3) = 500*n1 + 1000*n2 + 1500*n3.    ANSWER to (i)


     Part (i) is solved.



(ii)  The annual cost function is the function of three arguments (n1,n2,n3), 
      where n1 is the number of units of Model 1, n2 is the number of units of Model 2, 
      and   n3 is the number of units of Model 3 produced per year.


      The annual cost function is

          C(n1,n2,n3) = 25000000 + (175+100)*n1 + (400+150)*n2 + (750+225)*n3.    

                      = 25000000 +  275*n1     +    550*n2    +     975*n3.      ANSWER to (ii)


      Part (ii) is solved.



(iii)  The profit function is the function of three arguments (n1,n2,n3), 
       where n1 is the number of units of Model 1, n2 is the number of units of Model 2, 
       and   n3 is the number of units of Model 3 produced per year.


       The profit function is

           P(n1,n2,n3) = R(n1,n2,n3) - C(n1,n2,n3) = (500-275)*n1 + (1000-550)*n2 + (1500-975)*n3 - 25000000.    

                                                   =   225*n1     +   450*n2      + 525*n3 - 25000000.    ANSWER to (iii)

       Part (iii) is solved.

Solved completely.