SOLUTION: I need to double check if I did this word problem right. The question reads: A pizza shop makes $1.50 on each small pizza and $2.15 on each large pizza. On a typical Friday, it sel

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Question 164510: I need to double check if I did this word problem right. The question reads: A pizza shop makes $1.50 on each small pizza and $2.15 on each large pizza. On a typical Friday, it sells between 70 and 90 small pizzas and 100 and 140 large pizzas. The shop can make no more than 210 pizzas in a day. How many of each size of pizza can be sold in order to maximize the profit?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
What'd you get???
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Let S be the number of small pizzas, L the number of large pizzas.
The profit equation is
P=1.50%2AS%2B2.15%2AL
The bounding lines for the feasible region are,
70%3C=S%3C=90
100%3C=L%3C=140
S%2BL=210
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The x-axis is the number of small pizzas.
The y-axis is the number of large pizzas.
The black lines are the min and max values for each pizza type.
The red line is the max number of pizzas able to be made total.
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The vertices of the feasible region are shown as circles.
The min and max of the profit equation will occur at the vertices.
The coordinates for the vertices are
1.(70,100)
2.(70,140)
3.(90,100)
4.(90,120)
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P%5B1%5D=1.50%2A70%2B2.15%2A100=105%2B215=320
P%5B2%5D=1.50%2A70%2B2.15%2A140=105%2B301=406
P%5B3%5D=1.50%2A90%2B2.15%2A100=135%2B215=350
P%5B4%5D=1.50%2A90%2B2.15%2A100=135%2B258=393
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Max profit is $406 with 70 smalls and 140 larges.
Min profit is $320 with 70 smalls and 100 larges.