Is Objective functions 51S-(1/8)S^2 + 175D-(1/10)S^2 or 26S-(1/8)S^2 + 175D-(1/10)S^2 ?
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Is Objective functions 51S-(1/8)S^2 + 175D-(1/10)S^2 or 26S-(1/8)S^2 +

175D-(1/10)S^2 ?

Section 8.1 Expanded: Constructing the nonlinear profit contribution expression

Let PS and PD represent the prices charged for each standard golf bag and deluxe golf bag respectively. Assume that "S" and "D" are demands for standard and deluxe bags respectively.

S = 2250 - 15PS                                                                                                                                (8.1)

D = 1500 - 5PD                                                                                                                                 (8.2)

Revenue generated from the sale of S number of standard bags is PS*S. Cost per unit production is $70 and the cost for producing S number of standard bags is 70*S.

So the profit for producing and selling S number of standard bags = revenue - cost = PSS - 70S                       (8.3)

By rearranging 8.1 we get                        

15PS = 2250 - S or

                            PS = 2250/15 - S/15 or

                            PS = 150 - S/15                                                                                                                                (8.3a)

Substituting the value of PS from 8.3a in 8.3 we get the profit contribution of the standard bag:

                            (150 -S/15)S - 70S = 150S - S2/15 - 70S = 80S - S2/15                                                           (8.4)

Revenue generated from the sale of D number of deluxe bags is PD*D. Cost per unit production is $150 and the cost for producing D number of deluxe bags is 150*D.

So the profit for producing and selling D number of deluxe bags = revenue - cost = PDD - 150D                    (8.4a)

By rearranging 8.2 we get                        

5PD = 1500 - D or

                            PD = 1500/5 - D/5 or

                            PD = 300 - D/5                                                                                                                                   (8.4b)

Substituting the value of PD from 8.4b in 8.4a we get the profit contribution of the deluxe bags:

                            (300 -D/5)D - 150D = 300D - D2/5 - 150D = 150D - D2/5                                                       (8.4c)

By adding 8.4 and 8.4c we get the total profit contribution for selling S standard bags and D deluxe bags.

                            Total profit contribution = 80S -S2/15 + 150D - D2/5                                                                (8.5)

Homework assignment:

Reconstruct new objective function for 8.5 by changing "15PS" to "8PS" in 8.1, "5PD" to "10PD" in 8.2, cost per unit standard bag from 70 to "99" and cost per unit deluxe bag from 150 to 125. Keep other parameter values unchanged

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