The demand function for orange juice is q = 269

Question

The demand function for orange juice is q = 269 - 9p and the supply function is q = 9 + 4p, where q is the number of units sold per year and p is the price per unit, expressed in dollars.The government decides to support the price of orange juice at a price floor of $24 per unit by buying orange juice and destroying all that it has purchased.How many units must the government destroy per year?
A)52
B)56
C)25
D)61
E)57

Quizplus · Accepted Answer

To find the quantity the government must destroy, first, we calculate the quantity supplied and demanded at the price floor of $24. For the demand function, q = 269 - 9p, substituting p = 24 gives q = 269 - 9(24) = 269 - 216 = 53. For the supply function, q = 9 + 4p, substituting p = 24 gives q = 9 + 4(24) = 9 + 96 = 105. The government must destroy the difference between the quantity supplied and demanded, which is 105 - 53 = 52 units.