Solve the problem.
-The marketing research department of a large manufacturing company has determined that the demand equations for two major items it produces are given by p = 2,000 - 5x + 8y and q = 4,000 + 9x - 7y where p is the
Price of item A, q is the price of item B, x is the monthly demand for item A, and y is the monthly demand for
Item B. Find the total monthly revenue from items A and B when x = 15 and y = 5.
A) $20,565
B) $50,195
C) $49,975
D) $29,415

Question

Quizplus · Accepted Answer

To find the total monthly revenue, we need to multiply the price by the quantity for each item and then add them together. Thus, the total monthly revenue is:
(p)(x) + (q)(y)
Substituting the given values of p, q, x and y into the equation, we get:
(2,000 - 5x + 8y)(15) + (4,000 + 9x - 7y)(5)
= 30,000 - 75x + 120y + 20,000 + 45x - 35y
= $49,975
Therefore, the best choice is (C). To find the total monthly revenue, we need to multiply the price and demand for items A and B and add them up.

For item A: 
Price (p) = 2,000 - 5x + 8y 
Price when x = 15 and y = 5: 
p = 2,000 - 5(15) + 8(5) = $1,925

Demand (x) = 15 
Revenue for item A = p * x = $1,925 * 15 = $28,875

For item B: 
Price (q) = 4,000 + 9x - 7y 
Price when x = 15 and y = 5: 
q = 4,000 + 9(15) - 7(5) = $5,080

Demand (y) = 5 
Revenue for item B = q * y = $5,080 * 5 = $25,400

Total monthly revenue = $28,875 + $25,400 = $54,275

Therefore, the best choice is C, $49,975.

Solve the Problem. -The Marketing Research Department of a Large Manufacturing Company Has