Graph the system of constraints and find the value of x and y that maximize the objective function.

We want to maximize C, which is C= 7x - 3y. Let's explore our intuition regarding how this will look. We know that both y and x are greater than or equal to zero, which means -3y will be a negative number (or 0) and x is a positive number (or 0). We want to get x as big as possible, given the constraints, we want y to be zero, if possible 

We see that, based on the constraints, y is greater than or equal to zero, but it has no other minimum value established. We only know that y and x add up to 5, and that y is less than or equal to (1/5)x + 2. That means y could be 0 and still satisfy the constraints. 

In order to maximize C, we want to be 5 as possible and y to be zero:

C = 7 (5) - 3(0)

C=35

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.