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hram777 [196]
3 years ago
11

A manager must decide how many machines of a certain type to purchase. Each machine can process 100 customers per day. One machi

ne will result in a fixed cost of $2,100 per day, while two machines will result in a fixed cost of $3,900 per day. Variable costs will be $17 per customer, and revenue will be $45 per customer.
a. Determine the break-even point for each range. (Round your answers to the next whole number.) One machine Two machines
b. If estimated demand is 90 to 120 customers per day, how many machines should be purchased?
Business
1 answer:
vampirchik [111]3 years ago
7 0

Answer:

Instructions are below.

Explanation:

Giving the following information:

Each machine can process 100 customers per day. One machine will result in a fixed cost of $2,100 per day, while two machines will result in a fixed cost of $3,900 per day. Variable costs will be $17 per customer, and revenue will be $45 per customer.

To calculate the break-even point in units, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

<u>1 machine:</u>

Break-even point in units= 2,100/ (45 - 17)

Break-even point in units= 75 costumers

<u>2 machines:</u>

Break-even point in units= 3,900/ 28

Break-even point in units= 139 costumers

If the demand is from 90 to 120 costumers per day, the company should buy 1 machine. <u>With this level of demand, the company will not cover the costs of two machines. </u>

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3 years ago
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Suppose that a lumberyard has a supply of 10-ft boards, which are cut into 3-ft, 4-ft, and 5-ft boards according to customer dem
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Answer :

Some answers are attached below

Explanation:

a) Based on the information provided, below are the all possible sensible patterns the lumberyard may use to cut the 10-ft boards -

Pattern Number 3-ft boards 4-ft boards 5-ft boards Waste (<3-ft)

1                      3                   0                     0                       1                                                                        

2                                2                 1                          0                      0

3                             1                    0                           1                       2            

4                                 0                     1                          1                        1

5                           0                      2                           0                       2                  

6                      0                     0                            2                     0      

b) ILP Formulation

Objective Function

Minimize Number of 10 ft-boards to be cut

Z = x1+x2+x3+x4+x5+x6 where xi is the number of boards for pattern i

subject to constraints -

3x1+2x2+x3>=90 ----> 3-ft boards

x2+x4+2x5>=60 ----->4-ft boards

x3+x4+2x6>=60 ----->5-ft boards

Xi>=0 ---->Non-negativity constraint

Below is the excel solver formulation and solution -

The optimal number of Pattern 1,5,6 =0, Pattern 2,3 and 4 = 30

The minimum number of 10 ft-boards to be cut = 90

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