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Kisachek [45]
4 years ago
8

. A one-product firm estimates that its daily total cost function (in suitable units) is C (x) = x^3 - 6x^2 + 13x + 15 and its t

otal revenue function is R(x) = 28x. Find the value of x that maximizes the daily profit. (4 points)
Business
1 answer:
givi [52]4 years ago
8 0

Answer:

Value of x maximising profit : x = 5

Explanation:

Cost : C(x) = x^3 - 6x^2 + 13x + 15 ; Revenue: R(x) = 28x

Profit : Revenue - Cost = R(x) - C(x)

28x - [x^3 - 6x^2 + 13x + 15]  = 28x - x^3 + 6x^2 - 13x - 15

= - x^3 +  6x^2 + 15x - 15

To find value of 'x' that maximises total profit , we differentiate total profit function with respect to x & find that x value.

dTP/dx = - 3x^2 + 12x + 15 = 0 ► 3x^2 - 12x - 15 = 0

3x^2 + 3x - 15x - 15 = 0  ► 3x (x +1) - 15 (x + 1) = 0 ► (x+1) (3x-15) = 0

x + 1 = 0 ∴ x = -1   [Rejected, production quantity cant be negative] ;

3x - 15 = 0 ∴ 3x = 15 ∴ x = 15/3 = 5

Double derivate : d^2TP/dx^2 = - 6x + 12

d^2TP/dx^2  i.e - 6x + 12  at x = 5 is -6(5) + 12 = - 30+ 12 = -8 which is negative. So profit function is maximum at x = 5

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Answer:

7.44 %

Explanation:

The Yield to Maturity (YTM) is the Interest rate that makes the Present Value of Coupons and Principle equal the Market Price or Current Price of the Bond.

The Yield to Maturity can be calculated using a financial calculator as follows :

PV = - $100

N = (15 -2) × 2 = 26

PMT = ($100 ×  7.30%) ÷ 2 = $3.65

FV = $103

P/YR = 2

YTM = ?

Therefore, Inputting the values in the calculator as shown gives the Yield to Maturity is 7.44 %.

7 0
3 years ago
The payments a business makes for investing in capital expenses are known as Question 3 options: A) profits B) interest C) wages
rewona [7]
The answer for this question is A.
4 0
3 years ago
Mountain High Ice Cream Company transferred $68,000 of accounts receivable to the Prudential Bank. The transfer was made with re
horrorfan [7]

Answer:

Entries are given below

Explanation:

Calculations

Cash = ($68,000 x 90%) - ($68,000 x 2%)

Cash = $61,200 - $1,360

Cash = $59,840

Loss on sale = ($68,000 + $3,800) - ($59,840 +$5,800)

Loss on sale =  $71,800 - $65,640

Loss on sale = $6,160

Entries

                                                   DEBIT      CREDIT

Cash                                           $59,840

Loss on sale                              $6,160

Receivable from factor            $5,800

Recourse liability                                        $3,800

Receivables                                                  $68,000

4 0
3 years ago
Read this scenario, and then answer the question that follows. richard is excited to start his trucking business. after taking o
Damm [24]

Some potential economic consequences that Richard did not consider before making his decision are:

  • The cost of maintenance for used trucks.
  • The cost of gasoline from the town to the nearest city.
  • The location of the places that goods will be transported to and from.

<h3>What are economic considerations?</h3>

These are the factors that will affect the profitability and viability of a business.

In Richard's case, he needed to have considered various costs such as the higher cost of maintaining used trucks and the cost of gasoline that he will incur for living so far from big cities.

He also needs to consider the distance his trucks will have to travel to pick up good and deliver them.

Find out more on economic considerations at brainly.com/question/13721949.

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8 0
2 years ago
Nolte Co. has 4,800,000 shares of common stock outstanding on December 31, 2017. An additional 200,000 shares are issued on Apri
Artist 52 [7]

Answer:

3. 5,110,000 and 5,170,000

Explanation:

Number of shares to be used in computing basic earnings per share

= 4800000*12/12 + 200000*9/12 + 4800004/12

= 4800000 + 150000 + 160000

= 5,110,000

Number of shares to be used in computing dilute earnings per share

= 4800000*12/12 + 200000*9/12 + 4800004/12 + (6000000/1000)*40*3/12

= 4800000 + 150000 + 160000 + 60000

= 5,170,000

Therefore, The number of shares to be used in computing basic earnings per share and diluted earnings per share on December 31, 2018 is 5,110,000 and 5,170,000.

5 0
3 years ago
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