Question: Suppose that the total revenue function for a manufacturer is R(x) = 300 ln(x + 1), so the sale of x units of a product

Suppose that the total revenue function for a manufacturer is R(x) = 300 ln(x + 1), so the sale of x units of a product brings in about R(x) dollars. Suppose also that the total cost of producing x units is C(x) dollars, where C(x) = 2x. Find the value of x at which the profit function R(x) - C(x) will be maximized. Show that the profit function has a relative maximum and not a relative minimum point at this value of x.

Step by Step Solution

★★★★★

3.39 Rating (174 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We wish to maximize Rx Cx The only c... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Applied Calculus Questions!

1. Given the facts of the case, what communications do you believe Forrester & Loomis should have made with the audit committee with regard to the transactions with the vendor to comply with PCAOB AS...

Suppose that the total revenue function for a commodity is R = 36x - 0.01x2. (a) Find R(100) and tell what it represents. (b) Find the marginal revenue function. (c) Find the marginal revenue at x =...

Suppose that the total revenue function for a product is R(x) = 50x and that the total cost function is C(x) = 1900 + 30x + 0.01x2. (a) Find the profit from the production and sale of 500 units. (b)...

Suppose that the total revenue function for a commodity is R(x) = 25x - 0.05x2. (a) Find R(50) and tell what it represents. (b) Find the marginal revenue function. (c) Find the marginal revenue at x...

For a new product, a manufacturer set up an infrastructure which costs him $ 1,40,000 and variable cost is estimated as $ 125 for each unit of the product. The sale price per unit is fixed at $ 160....

For a new product, a manufacturer set up an infrastructure which costs him Rs 1,40,000 and variable cost is estimated as Rs 125 for each unit of the product. The sale price per unit is fixed at Rs...

Hi, kindly help me to answer below questions 3 and 5. Thanks! QUESTION 3 a) Find derivatives of the following functions i. Find ifs = (7+9)(#-9). (2.5 marks) ii. Find - if R(x) = 70x' +71x 2x + 2...

Briefly discuss the cost-volume-profit analysis model and how it is used. Use the attached PDF. APA Citation. 300 words. REVISED PAGES 3 Chapter Three 1 Fundamentals of Cost-Volume-Prot Analysis...

1. [-/3 Points] DETAILS HARMATHAP12 10.3.007.MI. MY NOTES Consider the following total revenue function for a hammer. R = 56x - 0.01x2 (a) The sale of how many hammers, x, will maximize the total...

Hi, you will find the instructions in the attached file, thank you, Using the regression results and the other computations from Assignment 1, determine the market structure in which the low-calorie...

MAT1050 / Dr. Khoule Exam 3 1. The total revenue function for a product is given by same product is given by R 250x C 1600 350x x 2 , and the total cost function for this , where R and C are each...

Lease Classification, Considering Firm Guidance (Issues Memo) Facts: On 1/1/20X1, Investor, Inc. (Lessee") signed a Lease Agreement with Developer Inc. (Landlord") to lease Landlord's newly...

Determine the total amount of adjustments to add to net income in order to compute cash flow from operating activities if the indirect method is used. 1. Goodwill impairment $400,000. 2. Issued...

Answer is not complete. 1 . TheMaster budgetselected answer correctis a set of interrelated budgets that constitutes a plan of action for a specific period . 2 . Thenot attemptedestablish goals for...

Toys R Us, Inc., is the leading store for childrens toys and other play material. The companys financial officer is determining the previous months sales revenues. The following data are a selection...

Perform the test in Problem 8.136, and report a two tailed p-value? Cancer Age at menarche (onset of menstrual periods) is an important risk factor for breast cancer and possibly ovarian cancer. In...

How many participants should be enrolled in each group in a future study, if (a) The true mean difference in age at menarche between girls with low- and high-childhood- SES is 0.5 year, (b) Standard...

Do boys with better glycemic control have different growth patterns in weight than boys with poorer glycemic control?

The following adjusted trial balance contains the accounts and balances of Cruz Company as of December 31, 2013, the end of its fiscal year. No. Account Title Debit Credit 101 Cash $ 18,000 126...

City Movers announced that its next annual dividend will be $.40 a share. Dividends will be $.60, and $.75 a share annually for the following two years, respectively. After that, dividends are...

Krall Company recently had a computer malfunction and lost a portion of its accounting records. The company has reconstructed some of its financial performance measurements including components of...