a) Express the total weekly costs C(x) as a function of the production level x.
C(x) = $70(x) - $1000
If Jill can sell her lawnmowers for $150 each,
b) Find the revenue function R(x)
c) Find the manufactures weekly profit function P (x)
d) How many lawnmowers must the producer sell per week in order to show profit?
2. The weekly cost of manufacturing x telephones per week is found by a manufacturer to be C(x) = 500 + 20(x) = x^2 dollars.
a) find the manufacturer's break-even production level(s)
b) for what production levels will the manufacturer experience a profit?
3) A cable television company estimates that with x thousand subscribers, its monthly revenue and cost (in thousands of dollars) are
R(x) =32x - 0.2x^2
Determine the company's break even points.
4) The cost C per unit time, of producing rum cakes for a particular manufacturer, is known to be linearly related to the production level.
That is C = mx + b, where x is the number of rum cakes produced is week, and m and b are constants.
The cost of producing 100 cakes per week is $600.
a)find m and b
b)find the cost of producing 150 cakes per week.
c) what is the manufacturers fixed weekly cost?
5) A microwave maufacturer sells microwaves to a certain retailer for $200
each, plus a handling charge of $75 on each order. The retailer applies a markup of 40% to the total price paid to the manufacturer.
a)find the function C(x), giving the retailers total cost of a single order of x microwaves.
b)show that the fuction R (x), giving the retailer's total revenues from the sale of these x microwaves is R(x) = 280x + 105 dollars.
c) if the retailer sells all these microwaves at the same price, what is the function for the retail price per microwave?
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