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Lunna [17]
1 year ago
10

a manufacturer makes two types of rubber, butadiene and polyisoprene. the plant has two machines, machine-1 and machine-2, which

are used to make the rubber strips. manufacturing one strip of butadiene requires 2.75 hours on machine-1 and 3 hours on machine-2. processing one strip of polyisoprene takes 3.5 hours on machine-1 and 4 hours on machine-2. machine-1 is available 180 hours per month, and machine-2 is available 200 hours per month. formulate an all-integer mathematical model that will determine how many units of each type of rubber should be produced to maximize profits if the profit contributions of butadiene and polyisoprene are $20 and $26, respectively.
Business
1 answer:
nignag [31]1 year ago
4 0

The all-integer model that determines how many units of each type of rubber should be produced to maximize profits is given by:

  • Maximize: P(x,y) = 20x + 26y.
  • Constraint 1: 2.75x + 3.5y ≤ 180.
  • Constraint 2: 3x + 4y ≤ 200.
  • Constraint 3: x ≥ 0, y ≥ 0.

<h3>How to maximize profit?</h3>

The profit is maximized using linear programming, for a system of equalities/inequalities, in which the variables are given as follows:

  • Variable x: number of units of butadiene produced.
  • Variable y: number of units of polyisoprene produced.

The profit contributions of butadiene and polyisoprene are $20 and $26, hence the profit function is defined as follows:

P(x,y) = 20x + 26y.

The number of units is a countable amount, hence the values of x and y should be positive, and the constraint is of:

x ≥ 0, y ≥ 0.

Machine-1 is available 180 hours per month, hence the constraint relative to machine-1, considering the time needed for each unit, is of:

2.75x + 3.5y ≤ 180.

Machine-2 is available 200 hours per month, hence the constraint relative to machine-2, considering the time needed for each unit, is of:

3x + 4y ≤ 200.

More can be learned about linear programming at brainly.com/question/14309521

#SPJ1

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Answer and Explanation:

a. The journal entries are shown below:

1) Cash Dr  (16,000 shares × $14) $224,000

        To Common stock (16,000 shares × $9) $144,000

        To Additional paid in capital - common  (16,000 shares × 5) $80,000

(Being the issuance of the common stock is recorded)

2 Cash Dr  (15,000 shares × $30) $450,000

        To Preferred stock (15,000 shares × $25) $375,000

        To Additional paid in capital - preferred  (15,000 shares × $5) $75,000

(Being the issuance of the preferred stock is recorded)

3) Cash Dr  (52,000 shares × $17) $884,000

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        To Additional paid in capital - common  (52,000 shares × $8) $416,000

(Being the issuance of the common stock is recorded)

We debited the cash to record this journal entries as it raised the assets and credited the common stock and additional paid in capital, as it also raised the equity of the stockholder

b. The preparation of the stockholder equity section of the balance sheet is presented below:

                          Stockholders' equity section of the balance sheet

Common stock  $612,000    ($144,000 + $468,000)

preferred stock $450,000

Additional paid in capital - preferred $75,000

Additional paid in capital - common   $496,000   ($80,000 + $416,000)

Total $1,633,000

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<h3>What is vertical integration?</h3>

Vertical integration is a procedure that entails acquiring corporate operations in order to produce the same thing.

  1. When a business chooses vertical integration, they typically have control over some phases of product production and delivery.
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5 0
2 years ago
Report a chef has a large container of olive oil. in one night, after he used 252525 quarts, 35.9\%35.9%35, point, 9, percent of
maks197457 [2]
He had a large container of 25 quarts. Then he used 25 quarts and 35.9% of the oil remained.
100% - 35.9% = 64.1%
25 quarts ------------------------- 64.1%
 x quarts  -------------------------- 100%
------------------------------------------------
25 : x = 64.1 : 100
64.1 x = 2,500
x = 2,500 : 64.1 = 39.00156 ≈ 39 quarts
39 - 25 = 14 quarts
Answer: 14 quarts of olive oil remained in the container.
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