The total weekly profit (in dollars) realized by Country Workshop in manufacturing and selling its rolltop desks is given by the profit function
Where x stands for the number of finished units and y denotes the number of unfinished units manufactured and sold each week. The company's management decides to restrict the manufacture of these desks to a total of exactly 100 units/week. How many finished and how many unfinished units should be manufactured each week to maximize the company's weekly profit?

A) 40 finished and 60 unfinished units
B) 60 finished and 40 unfinished units
C) 10 finished and 90 unfinished units
D) 50 finished and 50 unfinished units

Question

The total weekly profit (in dollars) realized by Country Workshop in manufacturing and selling its rolltop desks is given by the profit function ​  ​
Where x stands for the number of finished units and y denotes the number of unfinished units manufactured and sold each week. The company's management decides to restrict the manufacture of these desks to a total of exactly 100 units/week. How many finished and how many unfinished units should be manufactured each week to maximize the company's weekly profit?
​
A) 40 finished and 60 unfinished units 
B) 60 finished and 40 unfinished units 
C) 10 finished and 90 unfinished units 
D) 50 finished and 50 unfinished units

Quizplus · Accepted Answer

To maximize weekly profit, we need to use partial derivatives.

Let's find the partial derivative with respect to x:

∂P/∂x = 400 + 200y - 22x

Now let's find the partial derivative with respect to y:

∂P/∂y = 400 + 200x - 11y

To maximize profits, we need to set both the partial derivatives to zero:

400 + 200y - 22x = 0

400 + 200x - 11y = 0

Solving for x and y, we get:

x = 60 and y = 40

Therefore, the company should manufacture 60 finished and 40 unfinished units each week to maximize profit.

So, the answer is B.

The Total Weekly Profit (In Dollars) Realized by Country Workshop