Question

TeeVee Electronics, Inc., makes console and wide-

Answer 1

Answer:

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,