Question

Question 14 1 pts 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 - 5Qc Friday Building Demand: PF = 400 - 3QF The total number of jerseys (Q) available is 31. 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

Given:Pc = 240 - 5QcPF = 400 - 3QFTotal number of jerseys (Q) available is 31We need to find out the quantity of jerseys that should be allocated to the Friday Building using the following steps:First, we have to find out the total revenue function by multiplying the selling price with the total quantity of jerseys sold as follows:TR = PcQc + PFQFWhere TR stands for total revenue. We know that the total number of jerseys available is 31 and we need to allocate the quantity of jerseys to both places to maximize the total revenue.Since we need to allocate the quantity of jerseys to both places to maximize the total revenue, we have to use the constraints given by the number of jerseys available as follows:Qc + QF = 31We can re-arrange the above equation to find out Qc as follows:Qc = 31 - QFNow we can substitute Qc in terms of QF in the total revenue function as follows:TR = (240 - 5Qc)Qc + (400 - 3QF)QFTR = (240 - 5(31 - QF))(31 - QF) + (400 - 3QF)QFTR = -5QF² + 355QF + 3720To maximize the total revenue, we have to take the derivative of the total revenue with respect to QF and then set it to zero as follows:dTR/dQF = -10QF + 355 = 0-10QF = -355QF = 35.5But we can't sell partial jerseys, so we have to round it off to the nearest whole number.So, the quantity of jerseys that should be allocated to the Friday Building is 36.