Monte Carlo Simulation to Get an Estimate Essay

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Monte Carlo simulation to get an estimate of the total production cost that can be expected for the company. The key to understanding this simulation is that there are two sets of information -- the probabilities and the randomly-generated number. The random number is between 1 and 100, so there is the same amount of numbers as there are probabilities. The probabilities need to be broken down on the spreadsheet to match up with a cost. So for the materials costs, there is an 18% probability that the materials costs will be $33. Thus, any random number between 1 and 18 will reflect a materials cost of $33. There is a 23% probability that the materials cost will be $34. Thus, numbers 19-41 inclusive will mean that the materials cost will be $34 on the spreadsheet. The formula for materials costs would therefore be:

=IF ($C6

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According to Graph 1, the point at which profit is maximized would be where the flavor and nutrient lines meet, with both lying beneath the color line. At this point, the production level is 4X and 3.5Y. The usage of N. would be 30 at this level, the usage of F. would be 72 and the usage of C. would be 72. The total contribution at this level would be $270. See Appendix B for the spreadsheet solution.

D. The total contribution at this level would be:

4.5(40) + (3)(30)

180 + 90 = $270

Task 3.

A. The economic order quantity model seeks to determine the size of order that would allow the firm to minimize its total ordering and holding costs. The EOQ formula is as follows:

source: NSCU.edu

In this formula, the variables are as follows:

A = Demand for the year

Cp = Cost of placing a single order

Ch = Cost to hold the inventory for a single year.

All of these values are given.

A=18,000

Cp = $38

Ch = 26%

First, we calculate the numerator: 2*18,000*38 = 1,368,000

Then we divide by (.26)*12 = 3.12

Then we take the square root of that number in order to yield the EOQ: 662.16

This can be rounded to 662 or 663, since a partial unit cannot be ordered.

B. The economic production lot size model helps a company to determine the optimal level of production to reduce the costs related to both production set-up and holding inventory. The formula for the economic production lot size model is:

source: Wikipedia

where K = setup cost

D = demand rate

F = holding cost

X = demand rate / production rate

We know that D = 15,000; F = 28% and K = $84

X will be 15,000 / 60,000 = .25

First, we solve the numerator: 2*84*15000 = 2,520,000

Then we can solve the denominator = (0.28)(1-.25) = 0.21*19

So we have 2,520,000 / 3.99 = 631,578.94

And then we take the square root of this to derive the EPQ = 794.72, which can be rounded down to 795 units per run.

Task 4. A. 1. PERT assumes a beta probability distribution for time estimates (NetMBA.com, 2010). This means that the probabilities are 1/6 optimistic, 2/3 probable and 1/6 pessimistic. So for Activity A, the formula would be:

((2)+(4*3)+(4))/6 = Expected time to complete

Expected time to complete = 3

The formula for variance is: [ ( Pessimistic - Optimistic ) / 6 ]2

So the variance for Activity A would be [(4-2)/6] 2 = 0.111

The table 1.1 would look as follows, given this information:

PERT/CPM Analysis

Task Detail Table 1.1

Task

Preceding Activity

Optimistic Time to Complete

(weeks)

Probable Time to Complete

(weeks)

Pessimistic Time to Complete

(weeks)

Expected Time to Complete (weeks)

Variance

(weeks)

START

A

START

2

3

4

3

0.11

B

START

5

6

13

7

1.78

C

A

3

4

8

4.5

0.69

D

B

10

11

15

11.5

0.69

E

C

4

5

6

5

0.11

F

B

8

10

12

10

0.44

G

F

4

6

11

6.5

1.36

H

D, E

8

10

18

11

2.78

I

G

3

6

12

6.5

2.25

J

H, I

2.....

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