Help me understand these answers

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In summary, Janet is an artist who produces and sells prints of her artwork. She currently sells her prints for $17 each and sells 340 prints. However, for each 75 cent price increase, she will sell 10 fewer prints. To calculate her total costs, the formula is C(x) = 500 + 2(340 − 10x) where x is the number of 75 cent price increases. For her revenue, the formula is R(x) = (17 + 0.75x)(340 − 10x) where x is the number of 75 cent price increases.
  • #1
IntegrateMe
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Janet is an artist who produces and sells prints of her artwork. If Janet sells her prints for $17 each, then she will sell 340 prints. Janet is considering whether she should change the price. She takes a survey and concludes that for each price increase of 75 cents, she will sell 10 fewer prints.

1. Janet plans to produce exactly the number of prints that her survey predicts she will sell. Her costs include $2 per print, along with $500 in fixed costs. Find a formula for C(x), Janet’s total costs, in terms of x, the number of 75 cent price increases.

A: C(x) = 500 + 2(340 − 10x)

2. Find a formula for Janet’s revenue, R(x), in terms of x, the number of 75 cent
price increases.

A: R(x) = (17 + 0.75x)(340 − 10x)
 
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  • #2
For part A:
$500 in fixed costs, and on top of that it then costs $2 for each sold print.
The question says that she will print exactly how many she sells, and that she will sell 340 with no price increase, and 10 less for each 75c increase (hence the 340-10x)
Add all this up, and you should get the C(x) you listed.

Part B:
The revenue is the profit Janet will make. So it's the cost of each print*number of prints sold.
From part A you already know she sells 340-10x prints each time, so all that's left is to find the cost of each print.
The initial cost is in the question (17) and the cost changes by 75c much like the number of prints sold goes down (by a factor of x)
Add all this up and you should get the R(x) formula you listed.
 

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