Your college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x copies of an edition is given by C(x) = 80+ 0.10x + 0.001x² dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) = P'(x) = (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition. revenue $ profit $ marginal revenue $ marginal profit $ Interpret the results. The approximate loss per additional copy per additional copy Interpret your answer. ✓ from the sale of the 501st copy is $ (c) For which value of x is the marginal profit zero? X = copies The graph of the profit function is a parabola with a vertex at x = copies. , so the profit is at a maximum when you produce and sell

Please help with h.

A linear revenue function is R = 86x. (Assume R is measured in dollars.) (a) What is the slope m? m = Let C(x) = 7x + 550 and R(x) = 28x. (a) Write the profit function P(x). P(x) = (b) What is the marginal revenue MR? MR = What does the marginal revenue mean? ○ Each additional unit sold yields this many dollars in revenue. ○ If the number of units sold is increased by this amount, the revenue decreases by $1. ◇ Each additional unit sold decreases the revenue by this many dollars. ◇ If the number of units sold is increased by this amount, the revenue increases by $1. (c) What is the revenue received from selling one more item if 50 are currently being sold? $ What is the revenue received from selling one more item if 100 are being sold? $ (b) What is the slope m of the profit function? m = (c) What is the marginal profit MP? MP = (d) Interpret the marginal profit. ○ Each additional unit sold increases the profit by this much. ○ This is the smallest number of units that can be sold in…

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?

The cost, in dollars, to produce x designer dog leashes is C(x) R(x) 7x + 10, and the revenue function, in dollars, is - 3x? + 55x - Find the profit function. P(x) = -322 + 48x – 10 Find the number of leashes which need to be sold to maximize the profit. 8. Select an answer Find the maximum profit. 182 Select an answer > Find the price to charge per leash to maximize profit. Select an answer > V Select an answer What would be the be much for a leash? dogs too much money for a lea leashes dollars

On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results.   Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________.   Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.

The company AffordableStuff sells cell phones. The marginal cost for each cell phone is given by the equation C(x) = 0.01x² – 3x + 229. a is the number of cell phones manufactured and sold. The marginal revenue function is R(x) = 429 – 2.x. Both C(x) and R(x) are given in dollars. a) Where do these curves intersect? What do those intersection points mean? b) Find the area between the curves, using end points that make sense. Round to the nearest cent. c) What does the area under the curve mean in this case?

Problem 3 A furniture maker builds and sells wooden benches. The demand function for the benches is given by the function p = 1600 -x where p is the price per bench and x is the number of benches sold. The furniture maker also knows that the fixed costs for the business are $20,000 and each bench costs $75 to make. Part a) Create a function that represents revenue as a function of the number of benches produced and create a function that represents the cost as a function of the number of benches produced. Make sure to label your input and output variables. Part b) How many benches should be produced and sold in order to maximize revenue? What price should the furniture maker sell them? (Make sure to show your work) Part c) How many benches should be produced and sold in order to maximize profit? What is the maximum profit? (Make sure to show your work)

Total profit is defined as total revenue, R(x), minus total cost, C(x), and is given by the function P(x)=R(x)-C(x). Given R(x)=59x-0.4x^(2) and C(x)=2x+15, find each of the ollowing. P(x) R(80),C(80), and P(80)

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…