SOLUTION: A small manufacturing business is started. Initial cost is $3300.00 The product costs $4.50 to manufactured. A. Write a cost function where x represents the number of items man

Algebra ->  Functions -> SOLUTION: A small manufacturing business is started. Initial cost is $3300.00 The product costs $4.50 to manufactured. A. Write a cost function where x represents the number of items man      Log On


   

Question 964705: A small manufacturing business is started. Initial cost is $3300.00 The product costs $4.50 to manufactured.
A. Write a cost function where x represents the number of items manufactured.
b. What is the revenue function if each item sells for $10.50.
c. what is the profit function?
d. How many items must be manufactured and sold to earn a profit?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A small manufacturing business is started. Initial cost is $3300.00 The product costs $4.50 to manufactured.
:
let x = no. of items made
:
A. Write a cost function where x represents the number of items manufactured.
Cost function is the cost to make each item + the fixed cost
C(x) = 4.50x + 3300
:
b. What is the revenue function if each item sells for $10.50.
Revenue is total amt received for x no. of items
R(x) = 10.50x
::
c. what is the profit function?
Profit is revenue - the cost, R(x) - C(x)
P(x) = 10.50x - (4.50x + 3300)
:
d. How many items must be manufactured and sold to earn a profit?
When revenue exceeds the cost; R(x) > C(x)
10.50x > 4.50x + 3300
Solve for x
10.50x - 4.50x > 3300
6x > 3300
x > 3300/6
x > 550 item; a profit is made when 551 items are sold
:
It all makes sense, doesn't it??