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 expression for 8.5 by changing 15PS to 10PS in 8.1, 5PD to 7PD in 8.2, cost per unit standard bag from 70 to 75 and cost per unit deluxe bag 150 to 140. Use up to 2 decimal points accuracy.