4d. Calculate how much profit Khalifa will make in six months.

A manufacturer estimates that its product can be produced at a total cost of C(x) = 50,000 + 100x + x3 dollars. If the manufactu

timofeeve [1]

Answer:

The level of production x that will maximize the profit is: 22,966

Explanation:

C(x) = 50,000 + 100x + x³

R(x) = 3400x

P(x) = R(x) - C(x)

= 3400x - [50,000 + 100x + x³]

= 3400x - 50,000 - 100x - x³

= 3300x - 50,000 - x³ .................... (A)

P'(x) = 3300(1) - 0 - 3x²

= 3300 - 3x²

At a critical point, P'(x) = 0

∴ 0 = 3300 - 3x²

3x² = 3300

x² = 1100

x = ± $\sqrt{1100}$

P"(x) = -6x

P( $\sqrt{1100}$ ) = -6 ( $\sqrt{1100}$ ) < 0

by second derivative, 'P' max at x = $\sqrt{1100}$ = 33.17 (rounds)

since x = $\sqrt{1100}$ ,

recall that P(x) = 3300x - 50,000 - x³ from equation (A)

Therefore, Maximum Profit

P( $\sqrt{1100}$ ) = 3300 $\sqrt{1100}$ - 50000 - $\sqrt{1100} ^{3}$

= 3300(33.17) - 50,000 - 33.17³

= 109461 -50,000 - 36495.26

= 22,965.74

Maximum profit is 22,966 to the nearest whole number

5 0

3 years ago

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and co

babunello [35]

Based on the probability distributions of the funds and the correlation, the following is true:

Investment proportions would be 33% Equity and 67% debt.
Standard deviation would be 21.16%.

<h3>What would be the Investment proportions?</h3>

The expected return can be found as:

= (Return on stock x Weight of stock) + (Return on debt x Weight of debt)

As we already have the return as 12%, we can solve the formula for weights :

12% = (16% x Weight of equity ) + (10% x Weight of debt)

12% = (16% x W of equity ) + (10% x (1 - W of equity))

12% = 0.16W + 10% - 0.1W

2% = 0.06W

W = 2% / 0.06

= 33%

Equity is 33% so Debt is 67%.

<h3>What would be the standard deviation?</h3>

= √(Weight of stock ² x Standard deviation of stock ² + Weight of debt ² x Standard deviation of debt² + 2 x standard deviation of stock x standard deviation of debt x Correlation x weight of stock x weight of debt )

= √(33%² x 34% ² + 67%² x 25%² + 2 x 34% x 25% x 0.11 x 0.33 x 0.67)

= 21.16%

Find out more on portfolio standard deviation at brainly.com/question/20722208.

8 0

2 years ago

If the total for this month's credit purchases is $550 at 24% annual interest, what is the total balance for the month after one

Westkost [7]

Answer:

560

Explanation:

Thats your answer.

8 0

3 years ago

Read 2 more answers

Your firm is considering an investment that will cost $750,000 today. The investment will produce cash flows of $250,000 in ye

den301095 [7]

Answer:

3.241 years

Explanation:

In the payback, we analyze in how many years the invested amount is recovered. The computation is shown below:

In year 0 = $750,000

In year 1 = $250,000

In year 2 = $300,000

In year 3 = $300,000

In year 4 = $300,000

In year 5 = $100,000

And, the discounted rate of return is 10%

The discount factor should be computed by

= 1 ÷ (1 + rate) ^ years

where,

rate is 9%

Year = 0,1,2,3,4 and so on

Discount Factor:

For Year 1 = 1 ÷ 1.10^1 = 0.9091

For Year 2 = 1 ÷ 1.10^2 = 0.8264

For Year 3 = 1 ÷ 1.10^3 = 0.7513

For Year 4 = 1 ÷ 1.10^4 = 0.6830

For Year 5 = 1 ÷ 1.10^5 = 0.6209

So after applying the discounting rate, the cash flows would be

In year 0 = $750,000

In year 1 = $250,000 × 0.909 = $227,250

In year 2 = $300,000 × 0.8264 = $247,920

In year 3 = $300,000 × 0.7513 = $225,390

In year 4 = $300,000 × 0.6830 = $204,900

In year 5 = $100,000 × 0.6209 = $62,090

If we sum the first 3 year cash inflows than it would be $700,560

Now we deduct the $700,560 from the $750,000 , so the amount would be $49,440 as if we added the fourth year cash inflow so the total amount exceed to the initial investment. So, we deduct it

And, the next year cash inflow is $204,900

So, the payback period equal to

= 3 years + $49,440 ÷ $204,900

= 3.241 years

In 3.241 years, the invested amount is recovered.

7 0

4 years ago

Horten Sporting Goods Corporation makes two types of racquets, tennis and badminton. The company uses the same facility to make

Aneli [31]

Answer:

Horten Sporting Goods Corporation

TR BR

a. Cost per unit $66.98 $62.08

b. Price of Badminton Racquets = $80.70

Explanation:

a) Data and Calculations:

Tennis Badminton

Racquets Racquets

Units produced 70,000 30,000

Direct costs:

Direct materials $17.10 per unit $14.80 per unit

Direct labor 33.50 per unit 23.10 per unit

Category Estimated Cost Driver Amount of Cost Driver

Cost TR BR Total

Unit level $736,000 Number of inspection hrs 15,900 7,100 23,000

Batch level 353,800 Number of setups 83 39 122

Product level 152,500 Number of TV commercials 4 1 5

Facility level 630,000 Number of machine hrs 30,600 39,400 70,000

Total $1,872,300

Overhead Rates:

Inspection = $32 ($736,000/23,000) per inspection hour

Equipment setup = $2,900 (353,800/122) per equipment setup

TV commercials = $30,500 ($152,500/5) per commercial

Depreciation = $9 ($630,000/70,000) per machine hour

Overhead Allocation:

TR BR Total

Inspection = $32 $508,800 $227,200 $736,000

($32*15,900) ($32*7,100)

Equipment setup = $2,900 240,700 113,100 353,800

($2,900*83) ($2,900*39)

TV commercials = $30,500 122,000 30,500 152,500

($30,500 *4) ($30,500 *1)

Depreciation = $9 275,400 354,600 630,000

($9 * 30,600) ($9 * 39,400)

Total allocated expenses $1,146,900 $725,400 $1,872,300

Units produced 70,000 30,000

Overhead cost per unit $16.384 $24.18

Cost per unit:

TR BR

Direct materials $17.10 $14.80

Direct labor 33.50 23.10

Overhead cost 16.38 24.18

Total cost per unit $66.98 $62.08

Cost of Badminton = $62.08

30% markup = 18.62

Price = $80.70

7 0

3 years ago