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A faculty member sells Gatorade at UNC Charlotte football games
A faculty member sells Gatorade at UNC Charlotte football games. He finds that if he raises his selling price by $1, he sells 5 less bottles each week. He turns over the operation to a Managerial Economics student for a week. The goal is to maximize revenue since the faculty member has a vast supply of Gatorade, and any unsold bottles can be sold in future weeks. The student takes over the operation for a week. She says she sold 30 bottles at the last game, and that is the optimal quantity that maximized revenue.
What price did the student sell the Gatorade for?
Expert Solution
To find the quantity (Q) of Gatorade bottles that has to be sold to maximize the TR, we need to find for which Q, MR is equal to zero.
MR is a change in TR when more bottles of Gatorade is being sold, divided by a change in the number of sold bottles.
So, MR = TR from selling 35 bottles of Gatorade - TR from selling 30 bottles of Gatorade.
If MR = 0, then TR from selling 35 bottles of Gatorade = TR from selling 30 bottles of Gatorade.
TR = Q * P
TR from selling 30 bottles of Gatorade (optimal quantity) is equal to 30*P.
When Gatorade is sold at a $1 lower price (P - 1), 35 bottles are sold.
Therefore, TR from selling 35 bottles of Gatorade is equal to 35 * (P-1)
At MR = 0, TR from selling 35 bottles of Gatorade = TR from selling 30 bottles of Gatorade.
Therefore:
35 * (P - 1) = 30*P
35*P - 35 = 30*P
5*P = 35
P = $7.
Therefore, to maximize the TR, the student sold 30 bottles of Gatorade at the price of $7 each.
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