A firm’s price and cost equations are given by P = 200 - 0.2Q and TC = 40,000 + 45Q, respectively. Therefore, its profit maximizing level of output is

Consider the following cost function: Total Cost = 50+5Q^3 and demand curve Price= 5000-275*Q Given these functions, what would be the profit maximizing output?

The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30q2 − 12.85q + 20 + 400/q. The total cost function is C(q) =  1/30q3 – 12.85q2 + 20q + 400 . The profit function is Π(q)= –1/30q3 + 0.85q2 + 20q – 400 (i) Determine the level of output for which the firm’s profit is maximized. (ii) What is the firm's maximum profit?

Suppose that the inverse demand for aloe juice in Greece is given by P = 100 – 2Q, where P is the price per bottle (1000ml) of aloe juice and Q is the total quantity, i.e., number of bottles, supplied in the market. There are two aloe juice manufacturers in Greece, Aloe Health and Aloe Wealth, operating under similar cost conditions. Each manufacturer's cost function is C(q) = 4qi, i =1,2, where q¡ is the manufacturer's individual quantity produced and Q = qı + q2. (a) Based on demand conditions every year, they decide, independently of each other, the quantity of aloe juice that will be supplied, letting the market determine the price per bottle. Find the equilibrium price and each firm's profit in this market. %3D (b) Consider that the above two manufacturers form a cartel, agreeing to fix their total quantity in such a way that the market maintains a collusive price. For simplicity, the eventual cartel directory will determine the target total-quantity and price pair, and each firm…

For a certain company, the cost function for producing items is C (x) = 30 x + 150 and the revenue function for selling æ items is R(x) = -0.5(x - 100)2 +5,000. The maximum capacity of the company is 160 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C (x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! Answers to some of the questions are given below so that you can check your work. 1. Assuming that the company sells all that it produces, what is the profit function? P(x) = Hint: Profit = Revenue - Cost as we examined in Discussion 3. 2. What is the domain of P(x)? Hint: Does calculating P(x) make sense when x = -10 or x = = 1,000? 3. The company can choose to produce either 70 or 80 items. What is their profit for each case, and which level of production should they choose? Profit when producing 70 items = Number Profit when producing 80…

Suppose that the finance department of our favorite company, TVZ R US, determines that the total = 500+ 2x. The marketing department's cost of producing a amount of televisions is C (x) estimate of the demand function for televisions has not changed and remains p = 10 -0.01x. A) Write an equation for the profit of this company. B) Use the first derivative to find the marginal profit of the function you wrote in part A. C) Compute the second derivative and determine if the value you found in Part B is an absolute maximum or absolute minimum. D) Find the maximum profit of the company. E) At what price are profits maximized?

Suppose that the profit from the sale of Kisses and Kreams is given by the following, where x is the number of pounds of Kisses and y is the number of pounds of Kreams. P(x, y) = 10x + 6.6y - 0.001x² -0.025y² dollars You know from previous experience that, for such a profit function, profit will be maximized at the critical point of P(x,y). (a) Determine the amounts of Kisses and Kreams that will maximize profit. pounds of Kisses pounds of Kreams (b) What is the maximum profit? (Round your answer to two decimal places.) $

A demand of 230 banquet attendees can be expected at a dinner plate price of $80.00 each. A demand of 370 banquet attendees can be expected at a dinner plate price of $45.00 each. Catering Service A has a fixed cost of $1,800 and a marginal cost of $30 for each plate. Catering Service B has a fixed cost of $2,500 and a marginal cost of $22 for each plate. Costs for both caterers include the food, drinks, plates, utensils, tablecloths, glasses, crew, and cleanup. Dinner plates will only be sold as an entire unit. To justify company resources and to ensure the event will benefit the charity, the CEO insists the tickets be sold for no less than $40. All profits will go toward a charity of the committee's choosing. Additional spontaneous donation to the charity will be accepted the night of the banquet. Studies estimate that 5% will give $5, 23% will give $20, 18% will give $50, 7% will give $100, and 2% will give $500. Find the Profit function, P(x) , for each of the two possible…

A company’s demand and cost functions are given by p(q)=-0.05q+525andC(q)=q3 -7q2 +85q. What price should be set if marginal profit is $0 per item?

The Lead Zeppelin Company produces powered and steerable lighter-than-air craft. The company’s airships are specially lined and are therefore safer than normal dirigibles. The table below shows the weekly production of dirigibles, along with the associated Average Cost and Total Revenue figures (the Average Cost and Total Revenue figures are actually in thousands of dollars, so the $15 represents $15,000, but we have left off the zeros to save space).   Quantity Average Cost Total Cost Total Revenue 0  -- 0 $0 1 $15 15 $10 2 $9 18 $20 3 $8 24 $30 4 $8.50 34 $40 5 $9 45 $50 6 $10 60 $60 7 $12 84 $70   The Lead Zeppelin Company has decided that it will produce at least 1 dirigible. Now the question becomes, how many more dirigibles should it produce to make as much profit as possible?   Use the profit-maximizing rule to explain how many dirigibles the Lead Zeppelin Company should produce to…