Question

A company produces two kinds of golf balls, one that sells for $3 and one that sells for $2. The total revenue, in thousands of dollars, from the sell of x thousand $3 golf balls and y thousand $2 golf balls if found by R(x,y)=3x+2y The company determines that the total cost to produce both golf balls, in thousands of dollars is given by c(x,y)=2x

2
−2xy+y
2
−9x+6y+7 a) Determine how many each type of golf ball the company should produce and sell in order to maximize their profit (give the maximum profit equation) SHOW ALL WORK and give correct units measures for your final answers. b) Find the maximum profit c) Verify using the D(x,y) test. Be sure to interpret what the d-test values in context. Show all your work (clearly label) and give your final solutions in the space provided below. a) The Profit function is P(x,y)= Profit is maximized when they produce and sell $3 gold balls and $2 golf balls b) The maximum profit is. c) Verify using the D(x,y) test. Be sure to interpret what the d-test values meaning in context.

Answer 1

To find the maximum profit, we need to differentiate the profit function P(x, y) with respect to both x and y. Let's start with the profit function given: P(x, y) = 3x + 2y.

a) To maximize the profit, we need to find the values of x and y that make the partial derivatives equal to zero. So, let's differentiate the profit function:

∂P/∂x = 3
∂P/∂y = 2

Setting both partial derivatives equal to zero, we get:

3 = 0
2 = 0

Since these are contradictions, there is no critical point for maximum profit. This means that profit is not maximized by producing and selling a specific number of gold balls (x) and golf balls (y).

b) Since there is no maximum profit, the question of finding the maximum profit is not applicable.

c) As there is no maximum profit, the D(x, y) test is not relevant in this context. Therefore, we cannot interpret the meaning of d-test values because there are no d-values to consider.

Please let me know if there is anything else I can help you with.