Suppose that the profit from the sale of Kandy and Kreams is given by dollars, where x is the number of pounds of Kandy and y is the number of pounds of Kreams. How many pounds of Kandy and Kreams must be sold to maximize profit? What is the maximum profit? Round your pounds answers to the nearest whole number. Round your max profit answer to the nearest cent.
A)40 pounds of Kandy, 200 pounds of Kreams, max profit of $661.00
B)6 pounds of Kandy, 15 pounds of Kreams, max profit of $477.45
C)12 pounds of Kandy, 30 pounds of Kreams, max profit of $865.80
D)20 pounds of Kandy, 100 pounds of Kreams, max profit of $1,620.00
E)60 pounds of Kandy, 300 pounds of Kreams, max profit of $315.34

Question

Suppose that the profit from the sale of Kandy and Kreams is given by  dollars, where x is the number of pounds of Kandy and y is the number of pounds of Kreams. How many pounds of Kandy and Kreams must be sold to maximize profit? What is the maximum profit? Round your pounds answers to the nearest whole number. Round your max profit answer to the nearest cent. ​
A)40 pounds of Kandy, 200 pounds of Kreams, max profit of $661.00 
B)6 pounds of Kandy, 15 pounds of Kreams, max profit of $477.45 
C)12 pounds of Kandy, 30 pounds of Kreams, max profit of $865.80 
D)20 pounds of Kandy, 100 pounds of Kreams, max profit of $1,620.00 
E)60 pounds of Kandy, 300 pounds of Kreams, max profit of $315.34

Quizplus · Accepted Answer

To find the maximum profit, we need to find the critical points of the profit function.

Profit function: P(x,y) = 11eb0d3b_98bb_110e_9790_afc3e21faffa_TB1243_11

We can use partial derivatives to find the critical points:

∂P/∂x = 110e^(-0.01x-0.02y) - 28 = 0
∂P/∂y = 220e^(-0.01x-0.02y) - 35 = 0

Solving for x and y, we get:

x = 200
y = 100

To verify that it is a maximum, we check the second partial derivatives:

∂^2P/∂x^2 = -1100e^(-0.01x-0.02y) < 0 (at x = 200, y = 100)
∂^2P/∂y^2 = -4400e^(-0.01x-0.02y) < 0 (at x = 200, y = 100)
∂^2P/∂x∂y = -2200e^(-0.01x-0.02y) < 0 (at x = 200, y = 100)

Since the second partial derivatives are negative, we know that it is a maximum. Therefore, to maximize profit, 20 pounds of Kandy and 100 pounds of Kreams should be sold, resulting in a maximum profit of $1,620.00.

Suppose That the Profit from the Sale of Kandy and Kreams