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Revenue and Cost Calculations

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A manufacturer of small chain saws has determined:
R(x)=xp(x)=x(200-x/30)=200x-x^2/30
C(x)=7200+60x

Where x is the number of saws that can be sold at price $p per saw and C(x) is the total cost (in dollars) of producing x saws.
a. Find the marginal cost
b. Find the marginal revenue
c. What is the minimum number of saws sold for the company to break even?
d. Find the profit function and write its equation.
e. Find the marginal profit.
f. Find the number of saws produced that generate maximum profit.
g. What is the average cost per saw at maximum profit?
h. What is the maximum profit?

The problem is I have the worst time with derivatives and since I do not know how to simplify to get the equation for P(x)=R(x)-C(x), it makes completing a-h impossible since I do not know the correct equation. In previous problems I have done marginal profit. Is marginal cost and marginal revenue the same equation?

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Solution Preview

a. Find the marginal cost
Since C(x)=7200+60x, C'(x)=60. Hence marginal cost=60.

b. Find the marginal revenue
Since R(x)=xp(x)=x(200-x/30)=200x-x^2/30, R'(x)=200-x/15. Hence marginal revenue = 200-x/15

c. What is the minimum number of saws sold for ...

Solution Summary

The revenues and cost calculations are examined in the solution.

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Accounting equation with transactions analyzed on MS Excel file.

Please fill out the attached balance sheet using the company information provided in the Excel file.

The following are the transactions relating to the formation of Cardinal Mowing Services, Inc., and its first month of operations.
a. The firm was organized and the owners invested cash of $600.
b. The company borrowed $900 from a relative of the owners; a short-term note was signed.
c. Two lawn mowers costing $480 each and a trimmer costing $130 were purchased for cash. The original list price of each mower was $610, but a discount was received because the seller was having a sale.
d. Gasoline, oil, and several packages of trash bags were purchased for cash of $90.
e. Advertising flyers announcing the formation of the business and a newspaper ad were purchased. The cost of these items, $170, will be paid in 30 days.
f. During the first two weeks of operations, 47 lawns were mowed. The total revenue for this work was $705; $465 was collected in cash and the balance will be received within 30 days.
g. Employees were paid $420 for their work during the first two weeks.
h. Additional gasoline, oil, and trash bags costing $110 were purchased for cash.
i. In the last two weeks of the first month, revenues totaled $920, of which $375 was collected.
j. Employee wages for the last two weeks totaled $510; these will be paid during the first week of the next month.
k. It was determined that at the end of the month the cost of the gasoline, oil, and trash bags still on hand was $30.
l. Customers paid a total of $150 due from mowing services provided during the first two weeks. The revenue for these services was recognized in transaction f.
Required:
(a) Record each transaction in the appropriate columns. (Negative amount should be indicated by a minus sign. Enter the total of the expense column as a positive amount. Leave no cells blank - be certain to enter "0" wherever required. Omit the "$" signs in your response.)
Assets Liabilities
Transaction Cash + Accounts Receivable + Supplies + Equipment = Notes Payable + Accounts Payable + Paid-in Capital
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
Total

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