Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 200 .
A) 160,10
B) 116,21
C) 108,23
D) 100,25
E) 76,31

Question

Quizplus · Accepted Answer

Let the two positive real numbers be x and y. According to the problem, x + 4y = 200. We need to maximize the product xy. To do this, express y in terms of x from the given equation: y = (200 - x)/4. The product xy becomes x(200 - x)/4. To find the maximum value, differentiate this expression with respect to x, set the derivative equal to zero, and solve for x. The differentiation gives a quadratic equation, and solving it gives the value of x that maximizes the product. Substituting back, we find that x = 100 and y = 25 satisfy the conditions and maximize the product.

Find Two Positive Real Numbers Whose Product Is a Maximum