Question

jp computer produces both laptop and desktop computers laptop computer take up 2 cubic feet of space and desktop computer take up 5 cubic feet of space.The maximum capacity on the delivery truck is 800 cubic feet. Due to the demand, they need to load at least 300 laptop computers. they profit $225 on each laptop and $280 on each desktop computer. How many of each should they load on the truck to maximize profit?

Answer 1

Answer:

400 laptop computers and 0 desktop computers

Step-by-step explanation:

Let x be the number of laptop computers and y be the number of  desktop computers.

Laptop computer takes up 2 cubic feet, so x laptop computers take up 2x cubic feet of space. Desktop computer take up 5 cubic feet of space, so y desktop computers take up 5y cubic feet of space.

In total, they take 2x + 5y cubic feet.

The maximum capacity on the delivery truck is 800 cubic feet, thus,

$2x+5y\le 800$

Due to the demand, they need to load at least 300 laptop computers, so

$x\ge 300$

They profit $225 on each laptop , then they profit $225x on x laptops. They profit $280 on each desktop computer, so they profit $280y on y desktop computers.

Total profit is

$P=\ (225x+280y)$

Plot the system of inequalities (see attached diagram)

$2x+5y\le 800$

$x\ge 300$

The maximum profit will be at on of three vertices of the common region:

$P(300,0)=225\cdot 300+280\cdot 0=\ 67,500\\ \\P(300,40)=225\cdot 300+280\cdot 40=\ 78,700\\ \\P(400,0)=225\cdot 400+280\cdot 0=\ 90,000$