Investing is best for

O.J. Juice Company sells bags of oranges and cartons of orange juice. O.J. grades oranges on a scale of 1 (poor) to 10 (excellen

siniylev [52]

Answer:

max z = $0.3x_{1} + 0.45x_{2} + 0.3y_{1} + 0.45y_{2}$

Constraints

$x_{1} + x_{2} \leq 100,000$ (Grade 9 oranges)

$y_{1} + y_{2} \leq 120,000$ (Grade 6 oranges)

$2x_{1} - y_{1} \geq 0$ (Avg oranges in bags)

$x_{2} - 2y_{2} \geq 0$ (Avg oranges in juice)

$x_{1}\geq 0, x_{2} \geq 0, y_{1}\geq 0, y_{2} \geq 0$

Explanation:

Let the variables used be x and y

x representing oranges of grade 9

y representing oranges of grade 6

Now, let $x_{1}$ be the oranges used in each bag in lbs, and $x_{2}$ be oranges used in juice of grade 9 each.

Similarly let $y_{1}$ will represent oranges of grade 6 in bags, and $y_{2}$ will represent oranges in juice of grade 6

Now total oranges sold in bags

= $x_{1}$ + $y_{1}$

And their revenue in $ = 0.5 revenue - 0.2 expense = 0.3

Total profit from bag shall be

0.3 ( $x_{1} + y_{1}$ ) = 0.3 $x_{1}$ + 0.3 $y_{1}$

Similarly total oranges in juice shall be

= $x_{2} + y_{2}$

Profit shall be

$1.50 - $1.05 = $0.45

Total profit from juice shall be

$0.45 ( $x_{1} + y_{1}$ ) = $0.45 x_{2} + 0.45 y_{2}$

Profit shall maximise as

z = $0.3x_{1} + 0.45x_{2} + 0.3y_{1} + 0.45y_{2}$

Further constraint 1 shall be

Total amount of grade 9 oranges used shall be max 100,000 lb

$x_{1} + x_{2} \leq 100,000$

Constraint 2

Total amount of grade 6 oranges used shall be max 120,000 lb

$y_{1} + y_{2} \leq 120,000$

Constraint 3

Average quality of oranges sold in bag shall be 7

$\frac{9x_{1} + 6y_{1} }{x_{1} + y_{1} } \geq 7$

Accordingly,

$9x_{1} + 6y_{1} \geq 7x_{1} + 7y_{1}$

Simplifying:

$2x_{1} - y_{1} \geq 0$

Constraint 4

Average quality of oranges sold as juice shall be 8

$\frac{9x_{2} + 6y_{2} }{x_{2} + y_{2} } \geq 8$

Accordingly,

$9x_{2} + 6y_{2} \geq 8x_{2} + 8y_{2}$

Simplifying:

$x_{2} - 2y_{2} \geq 0$

Constraints shall be

$x_{1}\geq 0\\x_{2} \geq 0\\y_{1}\geq 0\\y_{2} \geq 0$

5 0

3 years ago

The following materials standards have been established for a particular product: Standard quantity per unit of output 5.3 pound

tatiyna

Answer:

Direct material quantity variance= $20,628.3

Explanation:

Giving the following information:

Standard quantity per unit of output 5.3 pounds

Standard price $14.10 per pound

Actual materials used in production 5,650 pounds

Actual output 790 units

To calculate the direct material quantity variance, we need to use the following formula.

Direct material quantity variance= (standard quantity - actual quantity)*standard price

Direct material quantity variance= (5.3*790 - 5,650)*14.1

Direct material quantity variance= $20,628.3

3 0

3 years ago

My neighbor’s lawn is overgrown. While I was mowing my own lawn, I cut hers, too. She offered to pay me but I would not take her

mario62 [17]

A suitible answer would be voluntary <span />

6 0

3 years ago

Read 2 more answers

Which of the following is a type of tort?

Scrat [10]

Answer:

b

Explanation:

6 0

3 years ago

Read 2 more answers

The records of Hollywood Company reflected the following balances in the stockholdersâ equity accounts at the end of the current

ExtremeBDS [4]

Answer:

1-a. We have:

Total dividend for noncumulative preferred stock = $5,000

Dividend per share for noncumulative preferred stock = $1.00 per share

Total dividend for common stock = $80,000

Dividend per share for common stock = $1.60 per share

1-b. We have:

Total dividend for cumulative preferred stock = $15,000

Dividend per share for noncumulative preferred stock = $3.00 per share

Total dividend for common stock = $70,000

Dividend per share for common stock = $1.40 per share

2. No, the statement of cash flows will NOT be affected differently under the two independent assumptions.

Explanation:

1. Determine the total and per share amounts that would be paid to the common stockholders and the preferred stockholders under the two independent assumptions.

1-a. The preferred stock is noncumulative.

Noncumulative preferred stock is a type of preferred stock that does not entitle holders to any dividends that are missed.

Therefore, we have:

Total dividend for noncumulative preferred stock = Dividend percentage * Par value * Number of noncumulative preferred shares outstanding = 10% * $10 * 5,000 = $5,000

Dividend per share for noncumulative preferred stock = Total dividend for noncumulative preferred stock / Number of noncumulative preferred shares outstanding = $5,000 / 5,000 = $1.00 per share

Total dividend for common stock = Amount to distribute - Total dividend for noncumulative preferred stock = $85,000 - $5,000 = $80,000

Dividend per share for common stock = Total dividend for common stock / Number of common shares outstanding = $80,000 / 50,000 = $1.60 per share

1-b. The preferred stock is cumulative.

Cumulative preferred stock refers to a type of preferred stock that entitles the holder to dividends that have been missed before common stockholders are paid.

Therefore, we have:

Total dividend for cumulative preferred stock = (Dividend percentage * Par value * Number of noncumulative preferred shares outstanding) * (1 + Number of years missed) = (10% * $10 * 5,000) * (1 + 2) = $15,000

Dividend per share for noncumulative preferred stock = Total dividend for noncumulative preferred stock / Number of noncumulative preferred shares outstanding = $15,000 / 5,000 = $3.00 per share

Total dividend for common stock = Amount to distribute - Total dividend for noncumulative preferred stock = $85,000 - $15,000 = $70,000

Dividend per share for common stock = Total dividend for common stock / Number of common shares outstanding = $70,000 / 50,000 = $1.40 per share

2. Will the statement of cash flows be affected differently under the two independent assumptions?

No, the statement of cash flows will NOT be affected differently under the two independent assumptions. This is because the total amount of cash that will be paid as dividend under the two independent assumptions will still remain the same at $85,000.

3 0

3 years ago