A company has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item that it makes has its own cost of $34. One month the company filled an order for 2400 of its tapestries, selling each item for $63. How much profit was generated by the order?
Set up Cost function C(t) where t is the number of tapestries:
C(t) = Cost per tapestry * number of tapestries + Fixed Cost
C(t) = 34t + 26000
Set up Revenue function R(t) where t is the number of tapestries:
R(t) = Sale Price * number of tapestries
R(t) = 63t
Set up Profit function P(t) where t is the number of tapestries:
P(t) = R(t) - C(t)
P(t) = 63t - (34t + 26000)
P(t) = 63t - 34t - 26000
P(t) = 29t - 26000
The problem asks for profit when t = 2400:
P(2400) = 29(2400) - 26000
P(2400) = 69,600 - 26,000
P(2400) = 43,600
Set up Cost function C(t) where t is the number of tapestries:
C(t) = Cost per tapestry * number of tapestries + Fixed Cost
C(t) = 34t + 26000
Set up Revenue function R(t) where t is the number of tapestries:
R(t) = Sale Price * number of tapestries
R(t) = 63t
Set up Profit function P(t) where t is the number of tapestries:
P(t) = R(t) - C(t)
P(t) = 63t - (34t + 26000)
P(t) = 63t - 34t - 26000
P(t) = 29t - 26000
The problem asks for profit when t = 2400:
P(2400) = 29(2400) - 26000
P(2400) = 69,600 - 26,000
P(2400) = 43,600