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November 22, 2014

November 22, 2014

Posted by **lola** on Tuesday, May 14, 2013 at 4:08am.

a) an expression that describes the price of each table, based on the number of reductions, is 95 – 2x , where x represents the number of $2 reductions in price. write a similar expression to describe the number of tables the carpenter can expect to sell, based on the number of reductions.

***I got that part… its 25+3x

b) Write an equation to describe the carpenter’s income as a product of the price of each table and the expected number of tables sold.

**I also found this part. Income= (95-2x) (25+3x) = 2375+235x -6x2

c)

The carpenter hopes to earn $3600 to pay for his time, materials, and sales booth, as well as make a small profit. Determine the number of $2 reductions he can apply to the price of the tables to make $3600. ?

- Math -
**Reiny**, Tuesday, May 14, 2013 at 9:12amSo you want

(95-2x) (25+3x) = 3600

2375+235x -6x^2 - 3600 = 0

6x^2 - 235x +1225 = 0

by the quadratic formula:

x = 6.19 or x = 32.9

check:

if x = 6, number sold is 25+18 = 43 ,

price of each = 95-12 = 83

income = 43(83) = $3569 , close enough to $3600

if x = 33 , number sold = 25 + 124

price of each = 95-66 = 29

income = 124(29) = $3596 , same profit

but he would have to work so much harder

so he should sell them at $83 and make 43 of them to get appr $3600

HOWEVER, if you want the max profit,

then

profit = 2375+235x -6x^2 - 3600

d(profit)/dx = 235 - 12x = 0 for a max of profit

12x = 235

x = 235/12 = appr 19.58

there should be 20 reductions of $2

Proof:

number sold = 25 + 60 = 85

price of each = 95 - 40 = 55

income = 85(55) = 4675

take one less, x = 19

number sold = 25 +57 = 82

price of each = 95 - 38 = 57

income = 82(57) = 4674 , ahh $1 less

take one more, x = 21

number sold = 25 + 63 = 84

price of each = 95 - 42 = 53

income = 84(53) = 4452 , ahh again less

To make around $3600

there should be 6 reductions of $2

to make a max profit, there should be 20 reductions of $2

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