Question 158647This question is from textbook college algebra
: 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.
B. Graph profit equation on the xy coordinate system.
C.What is the slope of the line in part b? whats the practical meaning of this slope?
D.Find the intersepts of the line in part b. what is the practical meaning of these intercepts?
I need help putting the #s in proper order and I have no idea how to find the slope is this where y=mx+b comes in? help me please, Student in trouble.
This question is from textbook college algebra
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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:
:
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 = 
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.
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