Question

Am sorry if that hard to read I can upload a new pic it needed.

Answer 1

Answer: C) 13

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Step-by-step explanation:

Refer to the graph below. The blue region is the set of (x,y) points that make every inequality mentioned to be true.

This region is a rectangle such that
`0 \le x \le 4` and
`-1 \le y \le 5`

So x spans from 0 to 4, while y spans from -1 to 5. We include both endpoints for each x and y interval.

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The corner points of the blue shaded region are:

• A = (0, -1)
• B = (0, 5)
• C = (4, 5)
• D = (4, -1)

which will be plugged into the equation P = 2x+y to see which produces the largest output.

Let's try point A

P = 2x+y

P = 2(0)-1

P = -1

Repeat for point B

P = 2x+y

P = 2(0)+5

P = 5

Then point C

P = 2x+y

P = 2(4)+5

P = 13

Finally point D

P = 2x+y

P = 2(4)-1

P = 7

We see that 13 is the largest P output value and it occurs when (x,y) = (4,5)

This is why choice C) 13 is the final answer.

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Here's another way to see why choice C is the answer.

We want 2x+y to be as large as possible. Therefore, we want both x and y to be as large as possible. This happens when (x,y) = (4,5) since this corner point is the most distant from the origin (0,0) and it's located in the first quadrant.

So x is largest when x = 4 and y is largest when y = 5. This leads to 2x+y = 2(4)+5 = 13 being the largest value of P.