Let P, and P, represent the prices charged for each standard golf bag and deluxe

Question

Let P, and P, 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 D= 1500- SP (8.2) Revenue generated from the sale of S number of standard bags is P,*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 PS-70S (8.3) By rearranging 8.1 we get 1SP, 2250-Sor P. 2250/15-S/15 or P- 150 S/15 (8.3a) Substituting the value of P, from 8.3a in 8.3 we get the profit contribution of the standard bag: (I 50-S/15)S-70S = 150S-S/15-70S = 80S- SV15 (8.4) Revenue generated from the sale of D number of deluxe bags is P"D Cost per unit production is S150 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-1S0D (8.4a) By rearranging 8.2 we get 5P,-1500-D or

Explanation / Answer

So here S=2250-8Ps and D=1500-10Pd..................(1)

cost per unit standard golf bag=10 => for S bags, cost is 10*S and profit = Ps S - 10S....(2)

cost per unit deluxe golf bag=125 => for D bags, cost is 125*D and profit = PD D - 10D....(3)

From 1,

S=2250-8Ps => 8Ps =2250-S => Ps =(2250-S)/8.....(4)

D=1500-10Pd=> 10PD=1500-D => PD=(1500-D)/10...(5)

From (2) & (4)

S-profit = Ps S - 10S = ((2250-S)/8)*S-10S=(2250S-S2-80S)/8 =(2170S-S2)/8

D-profit =PD D -125D=(((1500-D)/10)*D)-125D= (1500D-D2-1250D)/10 =(250D-D2)/10

Now, adding the above,

Total profit contribution = (2170S-S2)/8 + (250D-D2)/10

=271.25S - S2/8 + 25D - D2/10

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