Question

__Is Objective functions ____51S-(1/8)S^2 + 175D-(1/10)S^2 or 26S-(1/8)S^2 +__

__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 P_{S} and P_{D} 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 - 15P_{S} (8.1)

D = 1500 - 5P_{D} (8.2)

Revenue generated from the sale of S number of standard bags is P_{S}*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 = P_{S}S - 70S (8.3)

By rearranging 8.1 we get

15P_{S} = 2250 - S or

P_{S} = 2250/15 - S/15 or

P_{S} = 150 - S/15 (8.3a)

Substituting the value of P_{S} from 8.3a in 8.3 we get the profit contribution of the standard bag:

(150 -S/15)S - 70S = 150S - S^{2}/15 - 70S = 80S - S^{2}/15 (8.4)

Revenue generated from the sale of D number of deluxe bags is P_{D}*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 = P_{D}D - 150D (8.4a)

By rearranging 8.2 we get

5P_{D} = 1500 - D or

P_{D} = 1500/5 - D/5 or

P_{D} = 300 - D/5 (8.4b)

Substituting the value of P_{D} from 8.4b in 8.4a we get the profit contribution of the deluxe bags:

(300 -D/5)D - 150D = 300D - D^{2}/5 - 150D = 150D - D^{2}/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 -S^{2}/15 + 150D - D^{2}/5 (8.5)

**Homework assignment:**

Reconstruct new objective function for 8.5 by changing "15P_{S}" to "8P_{S}" in 8.1, "5P_{D}" to "10P_{D}" 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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