The profit p in dollars of selling x widgets and y gadgets is given by the function p(x, y)=7x+8y. which corner point of the shaded region will maximize the profit?

Step-by-step explanation:

The given function that models the profit is

Now, we have three coordinates that can be the maximum profit, we need to evaluate them.

For (10,30)

With 10 widgets and 30 gadgets, profits are $310.

For (15,25)

For 15 widgets and 25 gadgets, profits are $305.

For (20,15)

For 20 widgets and 16 gadgets, profits are $260.

Therefore, the pair that maximize profits is (10,30).

So, the right answer is D.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2