Compute the maximum product for two positive numbers with the property that the sum of the first plus three times the second is 3000.
A) 30,000
B) 25,000
C) 15,000
D) 750,000
E) none of these

Question

Quizplus · Accepted Answer

To maximize the product of two numbers x and y, given the constraint x + 3y = 3000, use the method of Lagrange multipliers or substitute y = (3000 - x)/3 into the product function P = xy. The maximum product occurs when x = 1500 and y = 500, giving a product of 1500 * 500 = 750,000.

Compute the Maximum Product for Two Positive Numbers with the Property