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Question 120834: A store can purchase shirts for $7 each. It has fixed costs of $2,500. Each shirt is sold for $18.
1. Write a linear equation for both cost and revenue.
2. Graph both cost line and revenue line.
3. Determine the break-even point.
4. If the store wants to make a profit of $2,000, how many shirts must it sell?
Textbook is McDougal Littell
Algebra 1
Chapter 5 Resource Book
Page 19
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A store can purchase shirts for $7 each. It has fixed costs of $2,500. Each shirt is sold for $18.
:
Let x = no. of shirts
:
1. Write a linear equation for both cost and revenue.
Cost:
The total cost consist of the fixed cost and the wholesale cost of each shirt.
C(x) = 7x + 2500
:
Revenue:
Consists of the number of shirts sold times the $18 retail price of each
R(x) = 18x
:
:
2. Graph both cost line and revenue line.
Cost line: y = C(x)
y = 7x + 2500; purple line
Revenue line:
y = R(x)
y = 18x; Green
Plot these x = 0 and x=300
Graphing these:
:
3. Determine the break-even point.
That will be where the graphs intersect, approx: x=230 shirts sold
You can find out exactly: Break even occurs when Revenue = Cost
18x = 7x+2500
Solve for x to find the exact break-even point
:
:
4. If the store wants to make a profit of $2,000, how many shirts must it sell?
Profit is Revenue - cost:
18x - (7x + 2500) = 2000; solve for x
18x - 7x - 2500 = 2000
18x - 7x = 2000 + 2500
11x = 4500
x = 4500/11
x = 409.1 or 410 shirts will make a 2000 profit
Check that:
18(410) - 7(410) - 2500
7380 - 2370 - 2500 = $2010, we can't sell a fraction of a shirt
:
Did this shed some light on this cost, revenue, profit, stuff.
Any questions?
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