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_SS 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 S²/15 70S = 80S S²/15 (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_DD 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 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 15P_S to 8P_S in 8.1, 5P_D to 10P_D in 8.2, cost per unit standard bag from 70 to 70+ 06 and cost per unit deluxe bag from 150 to 125. Keep other parameter values unchanged. Use up to 2 decimal points accuracy.