Andy C. answered • 12/24/17

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X is the number of beach hats

Y is the number of afghans

7X + 4Y = 68 ---> Y = (68-7x)/4 = (-7/4)X + 17

X+Y <=14 -------> Y <= 14 - X = -x + 14

Y<=11

F(x,y) = $21X + $9Y is the revenue function

The region is bounded above by the line y=11.

The region is bounded to the right by the line y = -x +14

Then by the linbe y = (-7/4)X + 17.

The region is bounded below by the x-axis and to the left

by the y-axis, since all quantities are positive and region

must be in the 1st quadrant.

(You can get a good picture of the critical region by

graphing these lines using a graphing calculator

or going to www.desmos.com and graphing them there)

The critical points are (0,11), (3,11), (4,10), abnd ( 68/7, 0)

Plugging these into the revenue function:

F(0,11) = 21*0 + 9*11 = 99

F(3,11) = 21*3 + 9*11 = 63+99 = 162

F(4,10) = 21*4 + 9*10 = 84 + 90 = 174

F(68/7,0) = 21*68/7 + 9*0 = 3*68 = 204

68/7 = 9 and 5/7 hats

She cannot make 10 hats,as that would exceed the 68 hour limit by 2 hours.

9 hats yields $189 in 63 hours.

With only 5 hours remaining, she can only make 1 afghan.

That would yield another $9, for a total of $198

9 hats and 1 afghan will yield $198 in 67 hours.