Question 158647
The Alpha shoe co. has determined the annual cost of making x pairs of its best
 selling shoes, a1, is $25 a pair, + $75,000 in fixed overhead costs. Each pair
 of shoes made is sold at $50 wholesale.
;
A.Find the equations that model the cost, the revenue, and the profit. Verify that all three equations are linear.
:
The cost equation; (cost per pair * no. of pairs (x) + fixed cost)
C(x) = 25x + 75000
:
Revenue is the total received from selling x shoes at $50 a pair
R(x) = 50x
:
Profit is Revenue - Cost: R(x) - C(x); using the 1st two equation:
P(x) = 50x - (25x+75000)
P(x) = 50x - 25x - 75000; change sign when you remove the brackets
P(x) = 25x - 75000 is the profit equation
:
:
B. Graph profit equation on the xy coordinate system. (P(x) = y)
:
Graph the equation y = 25x-75000,   
 scale: x: -5000 to +200000; y; -10000 to +300000: should look like this:
:
{{{ graph( 300, 200, -5000, 20000, -100000, 300000, 25x-75000) }}}
Note that no profit is made until the fixed cost ($75000) is exceeded
;
:
C.What is the slope of the line in part b? whats the practical meaning of this slope?
:
The equation y = 25x+75000;p it is in the form: y = mx+b
therefore the slope is 25; that means there is an increase of 25 for each
increase in the value of x, ($25 is made on each pair)
;
:
D.Find the intercepts of the line in part b. what is the practical meaning of these intercepts?
:
Regarding the y intercept at -75000, that means there is a negative $75000
even when 0 shoes are made;(x=0) 
:
Regarding the x intercept, that occurs when profit is 0 (y=0), we can find that
using the equation y = 25x - 75000
0 = 25x - 75000; (find x when y = 0)
25x - 75000 = 0
25x = +75000
x = {{{75000/25}}}
x = 3000 prs of shoes 
That means 3000 pairs of shoes must be made before it crosses from a loss to a profit. 0 profit (y) occurs when revenue = cost,
:
:
This should make sense to you, study each step, if you have a question, email me.