Homework Soursewhen a commodity is sold for x per item the number of items
when a commodity is sold for $x per item, the number of items sold is f(x). the item costs $5 to make
a) express the total profit in terms of x.
b) what is the rate of change of total profit as x changes.
c) if 1000 items sell when the price is $15 and if the number of items that are sold decreases by 200 for every $1 increase in price, find the rate of change of profit when the item price is $15
please show steps for c)
a) express the total profit in terms of x.
b) what is the rate of change of total profit as x changes.
c) if 1000 items sell when the price is $15 and if the number of items that are sold decreases by 200 for every $1 increase in price, find the rate of change of profit when the item price is $15
please show steps for c)
Solution
a) Profit = revenue - cost cost = number of items times cost per items to make = 4f(x) revenue = number of items times selling-cost per item = xf(x) Profit = revenue-cost = x f(x) - 4 f(x) = (x-4) f(x) b) Profit = (x-4) f(x) rate of change = 1 f(x) + (x-4)f\'(x)
