Calvin works at a facility which processes apples. It costs the facility $0. 68 to make either a jar of applesauce or a bottle of apple juice. Due to the nature of the process and contractual agreements, Calvin’s facility must make and sell three jars of applesauce for every two bottles of apple juice. A jar of applesauce sells for $2. 20, and a bottle of apple juice sells for $3. 15. If the facility has annual overhead costs of $368,500, not including production costs, how many bottles of apple juice will the facility have sold when it breaks even every year? Round to the nearest whole bottle, if necessary. A. 38,789 b. 77,579 c. 116,368 d. 167,500.

Answers

Answer 1

The number of bottles the facility requires to sell when it breaks is given by

a system of two simultaneous equations.

When the facility breaks even, it would have sold 77,579 bottles of apples juice.

Reasons:

The cost to make a jar of applesauce or a bottle of apple juice = $0.68

Number of jars of applesauce to be sold foe every 2 bottles of apple juice = 3 jars

The selling price for a jar of applesauce = $2.20

Selling price for a bottle of apple juice = $3.15

Annual overhead cost excluding production cost = $368,500

Required: Number of bottles of apple juice sold by the facility when it breaks even annually.

Solution:

Let J represent the number of bottles of apple juice sold, and let S represent the number of jars of apple sauce, by excluding the production cost, we have;

(3.15 - 0.68)·J + (2.2 - 0.68)·S = 368,500

S : J = 3 : 2

Which gives;

[tex]\displaystyle \frac{S}{J} = \mathbf{ \frac{3}{2}}[/tex]

[tex]\displaystyle S= \frac{3}{2} \cdot J[/tex]

Therefore;

[tex]\displaystyle (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot S = (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot \frac{3}{2} \cdot J = \mathbf{368,500}[/tex]

Which gives;

[tex]\displaystyle (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot \frac{3}{2} \cdot J = \mathbf{ \frac{19 \cdot J }{4} } = 368,500[/tex]

[tex]\displaystyle J = \frac{368,500 \times 4}{19} = \frac{1474000}{19}=77578\frac{18}{19} \approx 77,579[/tex]

The number of bottles of apple juice sold, J ≈ 77,579 bottles

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Answers

the solution:

(1): "q2" was replaced by "q^2".

Step by step solution :

STEP
1
:
Trying to factor by splitting the middle term

1.1 Factoring q2-4q-12

The first term is, q2 its coefficient is 1 .
The middle term is, -4q its coefficient is -4 .
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Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12

Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -4 .

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Root plot for : y = q2-4q-12
Axis of Symmetry (dashed) {q}={ 2.00}
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Answers

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Based on the amount being made by Manolo and Annalisa every day, the amount both made on the various days were:

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Doubt clarification - use comment section.

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