SOLUTION: A company distributes college logo sweatshirts and sells them for $45 each. The total cost function is linear, and the total cost for 80 sweatshirts is $3912, whereas the total cos

Question 1144592: A company distributes college logo sweatshirts and sells them for $45 each. The total cost function is linear, and the total cost for 80 sweatshirts is $3912, whereas the total cost for 240 sweatshirts is $6952.
what is the equation for the revenue function?
What is the equation for the total cost function?
Find the break even quantity.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A company distributes college logo sweatshirts and sells them for $45 each.
let x = no. sold
then the revenue function
R(x) = 45x
:
The total cost function is linear, and the total cost for 80 sweatshirts is $3912, whereas the total cost for 240 sweatshirts is $6952.
let b = the fixed cost of making the shirts
240x + b = 6952
80x + b = 3912
------------------subtraction eliminates b, find x
160x + 0 = 3040
x = 3040/16
x = $19 the cost to make each shirt
:
Find the fixed cost
80(19) + b = 3912
b = 3912 - 1520
b = $2392 is the fixed cost.
:
what is the equation for the revenue function?:
R(x) = 45x
What is the equation for the total cost function?
C(x) = 19x + 2392
Find the break even quantity.
Rev = cost
45x = 19x + 2392
45x - 19x = 2392
26x = 2392
x = 2392/26
x = 92 shirts to break even
:
:
Check this with 92 shirts
92(45) = $4140
92(19) + 2392 = $4140 also
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