functions word problem

Question

a shoe co is trying to find the best price for its shoes. when shoes priced at $75, 110 shoes are sold. after research co finds that every $7 increase will result in 15 fewer shoes being sold..

 

 

1)write equation to represent the revenue R in dollars as a function of x, the number of $7 increases

2)domain and range of revenue function

 

 

 

 

 

Answer 1

Hmmm.  I wrote this:

 

R = (75 + 7x)(110 - 15x)

 

if x, the number of added shoes (pairs?) = 0, then you have your original situation of 75 pairs x 110 dollars/pair = 8250

 

if x = 1, you have (82)(95) = 7790

 

if x = 2, you have (89)(80) = 7120

 

if x = 3, you have (96)(65) = 6240

 

if 4 = 4, you do it!

 

if x = 5, you do it!

 

if x = 6, you have (117)(20) = 2340

 

if x = 7, you have (124)(5) = 620

 

If x = any integer over 8, the price charged (110 - 15x) becomes a negative number.

 

Domain = possible x's; range = possible y's (R's)