Suppose a small bicycle manufacturer makes cheap bikes that sell for 180$ each. The total cost of producing x bikes (in $) is given by c(x)=6000+240x-0.8x^2, where x is up to 200 bikes.

a. Write down the revenue function.
b. Graph the cost and revenue functions on suitable scales, for x from 0 to 200.
c. Find the break even point: the number of units (to the nearest whole number) which need to be produced for the revenue=cost. Use algebra.
d. Find the profit function p(x), and use this to find the number of units which produces the maximum profit. (hint: the marginal profit might help)

Solution Summary

The solution shows how to find the cost, revenue, and profit functions for the bicycle manufacturer. It also shows how to find the break even point and maximize the profit.

An oligopolist, the Bramwell Corporation has estimated its demand function and total cost functions to be as follows:
Q=25-0.05P
TC=700+200P
Quanitites to be used 1 to 14
What will be the price and quantity if Bramwell wnat to
1) Maximize Profit
2) Maximize Revenue
3) Determine the maximum revenue and the maximum pr

Let R(q) = 1/100 x^2 be a revenue function and C(q) = sqrt(x) be a cost function for a particular business commodity.
a) Demonstrate that C(q) = R(q) at approximately q =21.544.
b) Determine the marginal cost and marginal revenue functions.
c) Suppose the supply and demand for this commodity equalize at q=25. Determine the

6. You are the manager of a monopoly, and your demandand cost functions are
given by P = 480 - 8Q and C(Q) = 500 + 4Q2, respectively.
- What price-quantity combination maximizes your firm's profits
- Calculate the maximum profits.
- Is demand elastic, inelastic, or unit elastic at the profit-maximizing price
quantity com

Total cost of producing goods. See attached for full description.
4. The total cost of producing q units of product is given by C(q) = q^3 - 60q^2 +1400q + 1000 for 0 < q <= 50; the product sells for $788 per unit. What production level maximizes profit? Find the total cost, total revenue,and total profit at this production

1. A company sells it's products in a market where the market price, p, is linked to the quantity sold, q, by the linear equation p=120-2q.
a) Calculate the market price if the company sells 50 units. What is the revenue equation and the revenue if company sells 50 units?
The company incurs fixed costs of $400 and an addit

2. The demandand cost functions for a company are estimated to be as follows:
P = 100 - 8Q
TC = 50 + 80Q - 10Q2 + 0.6Q3
a) What price should the company charge if it wishes to maximize its profit in the short-run?
b) What price should it charge if it wishes to maximize revenue in the short-run?

You are given two points representing the number of items sold at a particular price. From these two points, a linear demand function is constructed. You are also given information on the cost of each item so that you can construct a cost function. From the demand function you can form a revenue function and finally the profi

A health club has cost and revenue functions given by C = 10,000 + 35q and R = pq, where q is the number of annual club members and p is the prices of a one year membership. The demand function for the club is q = 3000 - 20q.
a. Use the demand function to write cost and revenue functions of p.
b. Graph cost and revenue as

If total cost in $ is given by C(x) = 2x^2 + 4x + 50 and total revenue in $ is given by R(x) = 100x where x is units, find the
a. Profit function:
b. Marginal Profit Function:
c. x that maximizes profit:
d: Maximum Profit: