Question

TeeVee Electronics, Inc., makes console and wide-

screen televisions. The equipment in the factory allows +

for making at most 450 console televisions and 200

wide-screen televisions in one month. It costs $600 per

unit to make a console television and $900 per unit to

make a wide screen television. The profit on each

console television is $125 per unit, while the profit for

each wide screen television is $200 per unit. During the -

month of November, the company can spend $360,000 to make these televisions. To

maximize profits, how many of each type should they make?

LET

Answer 1

First we need to put all the given information in a table, that way we'll express it better into inequalities.

Cost Production Max.

Console screen (x) $600 450

Wide-screen (y) $900 200

$360,000

We have:

`600x+900y \leq 360,000`

Because they can't spend more than $360,000 in production.

`x\leq 450\\y\leq 200`

Because the number of television is restricted.

The profit function is

`P(x,y)=125x+200y` (this is the function we need to maximize).

First, we need to draw each inequality. The image attached shows the region of solution, which has vertices (0,200), (300,200), (450, 100) and (450,0).

Now, we test each point in the profit function to see which one gives the highest profit.

For (300,200):

`P(300,200)=125(300)+200(200)=37,500+40,000=77,500`

300 console screen and 200 wide screen give a profit of $77,500.

For (450,100):

`P(450,100)=125(450)+200(100)=56,250+20,000=76,250`

450 console screen and 100 wide screen give a profit of $76,250.

Therefore, to reach the maximum profits, TeeVee Electronic, Inc., must produce 300 console screen televisions and 200 wide-screen televisions to profit $77,500,