Suppose the revenue function y=R(x) is linear, and points (x,y) of (10,550) and (13,715) are on the line. a. What is the marginal revenue? b. Suppose also the total costs are given by C(X) = 150 + 15x +2x^2. Find the x-value that maximizes profit.

Suppose the revenue function y=R(x) is linear, and points (x,y) of (10,550) and (13,715) are on the line. a. What is the marginal revenue? b. Suppose also the total costs are given by C(X) = 150 + 15x +2x^2. Find the x-value that maximizes profit.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 2E

See similar textbooks

Related questions

Q: Nana sells homemade yoghurt tubs at 75 pesos per tub. Suppose x bottles of sanitizer are produced…

Q: The cost function for a firm is given by CQ) = 5 + Q If the firm sells output in a perfectly…

A: Perfectly competitive market: - it is a market condition where there are many buyers and many…

Q: a. Find the input demand (x), output supply (y), and profit function for the technology, y = ln(x),…

A: Hotelling's lemma is a result in microeconomics that relates the supply of a decent to the greatest…

Q: Show that the profit function is convex in (p, w)

A: Consider the definition of a convex function. A function f: Rm+n → R1 is said to be convex iff ( λ…

Q: A demand curve is given by p = 660-3x. Assume you must pay salaries totalling 8000$ in a month.…

A: We are going to use Single variable maximisation method to answer this question.

Q: A firm has the following demand and average total cost functions: Q = 30 – P 7 1 - 6 +-Q ATC = - -…

Q: Given the total revenue and the total cost function in # 18, the corresponding marginal revenue is…

A: The firms, and businesses in the market tend to operate as sellers. These firms make various goods,…

Q: Suppose the firm achieves total revenue of $1,000 by selling 150 units while facing total costs of…

A: The marginal revenue must be compared to the marginal cost of production to know if the firm must…

Q: Write out the total cost and total revenue functions in terms of Q.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The total revenue curve of a firm is R (q) = 40q - 12q2 and its average cost A(q) = 1/30q2 - 12.85q…

A: Total revenue, R (q) = 40q - 12q2 Average cost, A(q) = 1/30q2 - 12.85q +20 + 400/q

Q: The fixed cost is $150, the variable cost per unit $5, and the demand function fo a the product is…

A: The goal of any firm is profit maximization. Profit is nothing but the difference between total…

Q: Find the marginal profit function if cost and revenue are given by C(x) = 183 + 0.3x and R(x) = 9x -…

A: Marginal profit function measures how much the profit changes when there is a unit change in the…

Q: 8. (a) At a health food manufacturing plant, it costs $20000 to produce 1500 cases of tofu, and…

A: (a) The linear cost function could be written as : Y = Ax + B Y = Total cost Ax = Variable cost,…

Q: A firm's demand function is Q = 16 – P and its total cost function is defined as TC = 3 + Q +…

A: Profit depends on total revenue and total cost of a firm. Profit is a difference between total…

Q: Suppose a product's revenue function is given by R(q) = 3q + 700g . Find an expression for the…

A: The marginal revenue is calculated by differentiating the total revenue. Marginal revenue measures…

Q: The total revenue curve of a firm is R (q) = 40q - 12q2 and its average cost A(q) = 1/30q2 - 12.85q…

A: Total revenue, R (q) = 40q - 12q2 Average cost, A(q) = 1/30q2 - 12.85q +20 + 400/q

Q: A firm has the following demand and average total cost functions: Q = 30 − P ATC =7/Q− 6 +1/2 Q…

A: Q = 30 − P P = 30-QATC =7/Q− 6 +1/2 Q Total Revenue (TR) = PXQ = 30Q-Q2 Total Cost (TC) = ATCXQ TC…

Q: Sergio Lopez is a publisher of Latin American poetry. His fixed cost is $525, and the cost to…

A: Fixed cost is $525, and the cost to produce each individual copy of his book is $3.50. A linear…

Q: Suppose that the demand functions facing a n product firm are as follows: Q, = 40 – 2P, + P2 %D Q2 =…

A: The following problem has been answered as follows:

Q: he total revenue curve of a firm is R(q)=40q−12q and its average cost A(q)=130q−12.85q+20…

A: Hi, thank you for the question. As per our Honor code, we are allowed to attempt only first 3 sub…

Q: A firm has the following demand and average total cost functions: Q = 30 − P ATC =7/Q− 6 +1/2Q…

A: The total revenue of a firm is the total payment it receives from the sale of goods and services.…

Q: Suppose a product's revenue function is given by R(q)=−4q^2+500q Find an expression for the…

A: Meaning of Marginal Revenue: The term marginal revenue refers to the situation under which the…

Q: The total cost of a firm is TC(Q)=4Q2+6Q+34. Accordingly, its marginal cost is 2*4*Q+6 when its…

A: Answer to the question is as follows :

Q: A demand curve is given by p = 660-3x. Assume you must pay salaries totalling 8000$ in a month.…

A: We are going to solve this question using single variable maximisation method.

Q: A firm's demand function is Q = 16 - P and its total cost function is defined as TC = 3 + Q + 0.25Q²…

A: Economic profit is the difference between total revenue and total cost.

Q: A demand curve is given by p = 660-3x. Assume you must pay salaries totalling 8000$ in a month.…

A: We are going to use single variable profit maximisation method to answer this question.

Q: Teddy J is a manufacturer of dish washing liquid. If his monthly demand function for 750ml size is…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Suppose the cost function for a firm is given by C(Q) = 100 + Q2. If the firm sells output in a…

A: In a perfect competitive market all firms are price taker and keep their price level equal to the…

Q: Find the marginal profit function if cost and revenue are given by C(x) = 190 + 0.6x and R(x) = 7x -…

A: Answer to the question is as follows:

Q: A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500…

A: Given: Fixed Cost = $100 Total Cost = $2500 Output= 15 sinks q=15demand functionq=360 - p15=360 -…

Q: The total revenue curve of a firm is R (q) = 40q - 12q2 and its average cost A(q) = 1/30q2 - 12.85q…

A: Total revenue, R (q) = 40q - 12q2 Average cost, A(q) = 1/30q2 - 12.85q +20 + 400/q

Q: A firm's demand function is Q = 16 - P and its total cost function is defined as TC = 3 + Q+ 0.25Q²…

A: The main objective of every firm is to maximize its profits. Profits are the excess of revenue…

Q: Your college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x…

A: Given information P= 90cent =$.9 C=50+.10X+.001X2

Q: Given that the cost function MC=x-2x^2-1 and the revenue function as MR=2x^2-3x-1 .Assuming pure…

A: The firms refer to their cost and the revenue statements for knowing the estimated future. The firms…

Q: The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30q2 − 12.85q +…

A: Solution - Given in the Question - Total Revenue curve of a firm R(q) = 40q -12q2…

Q: The cost, in dollars, to produce x designer dog leashes is C(x) R(x) = 7x + 10, and the revenue…

A: Profit = TR - TC Where TR = Total Revenue TC = Total Cost Profit = -3x2 + 55x - 7x - 10 Profit =…

Q: When economists talk about a barrier to entry, they are referring to a.the downward-sloping portion…

A: The hindrances that make it difficult for a firm to enter a certain market such as, government rules…

Q: A firm's demand function is Q = 16 – P and its total cost function is defined as TC = 3 + Q + 0.25Q2…

A: Equilibrium in economics is the state of stability and balance. Any deviation from this level will…

Q: Assume a firm's marginal costs are increasing at its current level of output. If a firm's marginal…

A: Marginal costs are the costs that measure the change in the total cost of production when the…

Q: Suppose the cost function for a firm is given by C(Q) = 100 + Q°. If the firm sells output in a…

A: In a perfectly competitive market at a price of $10, the firm should produce to maximize profits or…

Q: Your college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x…

A: C (x) = 10 + 0.10x +0.001x2 Price = 90 cents Total Revenue (TR) = Price * Quantity TR = 0.90 x

Q: A firm's marginal revenue and marginal cost functions are given by MR=10-4Q and MC= 1. If fixed…

A: The marginal cost is the adjustment of the complete expense that emerges when the amount delivered…

Q: Suppose the marginal cost and marginal revenue (in ¢000) for a product produced by a company is…

A: Given: MC=q+35 (in ¢000) MR=560+22q−q2 (in ¢000)

Q: Suppose an avocado farm has cost C= 0.004q + 28q + 1250, (where q is measured in bushels) and the…

A: A competitive market consist of large number of small firms and industry that determines price…

Q: The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30 q2 − 12.85q…

A: total revenue (TR) is defined as the total quantity(q) of commodity produced multiplied with its…

Q: Write down the revenue function, cost function, and profit function as functions of p. How much…

A: An economic Profit is the difference between the revenue a business has received from its outputs…

Question

Suppose the revenue function y=R(x) is linear, and points (x,y) of (10,550) and (13,715) are on the line.

a. What is the marginal revenue?

b. Suppose also the total costs are given by C(X) = 150 + 15x +2x^2. Find the x-value that maximizes profit.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

Suppose the marginal cost of producing x units of a product is given by: MC=4x+50 And the marginal revenue is given by: MR = 500 And the cost of the production and sale of 10 units is $1000. What is the profit function for this product ?
The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30 q2 − 12.85q + 20 + 400/q , ,where q is the firm's output. Is the rate of change of profit increasing or decreasing when the output level of the firm is 10 units?
The demand function for small high-definition televisions is given by p = 9,000 − 55x, where p is the price, in dollars, that x televisions can be sold. The cost function (in dollars) to produce televisions is C = 3,500x + 2,000. (Simplify your answers completely.) (a)Find the revenue function, R. R = (b)Find the profit function, P. P = (c)Find how many televisions should be sold to maximize profit. televisions (d)What is the maximum profit (in dollars)? $
Sergio Lopez is a publisher of Latin American poetry. His fixed cost is $525, and the cost to produce each individual copy of his book is $3.50. Currently, Sergio is selling these books for $6 each. So far this year, he has produced x a. Write a linear cost function C for Sergio’s book production, in terms of x. b. Find the linear revenue function R for selling x copies of the book. Remember that P(x) = (price)x. c. Use and 1b. to determine the profit function P for selling x books. Write the formula in simplified form. d.Use your answer for 1c to determine the profit, in dollars, for selling 300 books.
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)
A firm's demand and total cost function are given by the expression: P = 20 - Q/2 (1) TC = 0.5Q2 + 36 (2) Where P is price per unit in £ TC = total cost in £ Q is quantity demanded and produced. Find the profit-maximising level of output using the profit function and calculate how much profit is made at this output level.
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, where q is the firm's output. (1) Derive and expression C(q) for the firm's total cost function.
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) Is the rate of change of profit increasing or decreasing when the output level of the firm is 10 units?
The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30 q2 − 12.85q + 20 + 400/q , ,where q is the firms output. Derive expressions for the firm's: (i) total cost function (ii) total profit function
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, where q is the firm's output (1) Derive an expression Π (q) for the firm's profit function
A firm has a cost function of C = 1000 + 20Q + 1/10Q2a) Estimate the firm’s demand function. You may assume that the slope is a wholenumber, and the intercept is a multiple of 10. b) Find the firm’s revenue function. You do not need to draw it. c) Find the marginal revenue function, and draw it on a copy of the graph. d) Find and draw the marginal cost function.e) Use your results from parts (c) and (d) to find the profit-maximising level of output.(3 marks)f) Find the market price at this level of output.
A manufacturer of mountain bikes has the following marginal cost function: C′(q)=700/0.5q+2 where qq is the quantity of bicycles produced. When calculating the marginal revenue and marginal profit in this problem, use the approach given for the marginal cost and marginal revenue in the discussions in your textbook. a) If the fixed cost in producing the bicycles is $3200, find the total cost to produce 35 bicycles.Answer: $ b) If the bikes are sold for $250 each, what is the profit (or loss) on the first 35 bikes?Answer: $ c) What is the marginal profit on bike number 36?Answer: $