Question

Some UNCC students are selling Cam Newton autographed jerseys. They are selling them at two locations: the Cone Center and the Friday Building. They want to maximize total revenue, but the number of jerseys available is a constraint. Here are the two demand equations, where the Q's are the jerseys to be sold in each location: Cone Center Demand: PC = 240 - 6Qc Friday Building Demand: PF = 400 - 4QF The total number of jerseys (Q) available is 40. What quantity of jerseys should be allocated to the Friday Building? Enter as a value. ROUND TO THE NEAREST WHOLE NUMBER (CAN'T SELL A PARTIAL JERSEY).

Answer 1

Solution:

Since, we have a constraint of 40 jerseys only, we know that total number of jerseys in the two buildings should add up to 40.

Qf + Qc = 40

Qc = 40 - Qf

Then, total revenue = price of cone center Jersey*cone center jerseys + price of Friday building Jersey*friday building jerseys

TR = Pc*Qc + Pf*Qf

TR = (240 - 6*(40 - Qf))*(40 - Qf) + (400 - 4*Qf)*Qf

TR = 240*Qf - 6*Qf² + 400*Qf - 4*Qf²

Then, taking the first order condition to find Qf value maximizing the total revenue: dTR/dQf = 0

dTR/dQf = 240 - 6*2*Qf + 400 - 4*2*Qf

= 640 - 20*Qf

Then, dTR/dQf = 0 gives us 640 - 20*Qf = 0

Qf = 32

So, 32 jerseys should be allocated to the Friday building.