Goop Inc needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be Normally distributed with a mean of 250 gallons and a standard deviation of 125 gallons. Goop sells the polymer for $25 per gallon. Goop’s purchases raw material for $10 per gallon and Goop must spend $5 per gallon to dispose of all unused raw material due to government regulations. If demand is more than Goop can make, then Goop sells only what they made and the rest of demand is lost.Suppose Goop wants to ensure that there is a 92% probability that they will be able to satisfy the customer's entire demand. How many gallons of the raw material should they purchase? *Use Table in image and round your answer to the nearest integer. -4.0-3.9-3.8-3.7-3.6-3.5-3.4-3.3-3.2-3.1-3.0-2.9-2.8-2.7-2.6-2.5-2.4-2.3-2.2-2.1-2.0-19-1.8-1.7-1.6-15-1.4-1.3-12-1.1-1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.101234567891.01.11.21.31.41.51.61.71.81.92.02.12.22.32.42.52.62.72.82.93.03.13.23.33.43.53.63.73.83.9F)0000000000010001000200020003.000500070010001300190026003500470062008201070139017902280287035904460548066808080968115113571587184121192420274330853446382142074602500053985793.6179655469157257.758078818159.841386438849903291929332945295549641971397729821986198939918993899539965.997499819987999099939995999799989998999999991.0000400000000000000000000000100010001000200030004000500080011001500200027003700490065008501110143018302320293036704550561068608331004120214291687197823042668306935093989450950695668630469787687842992021.000410833116861.25611.34551.43671.52931.62321.71831.81431.91112.00852.10652.20492.30372.40272.50202.60152.70112.80082.90053.00043.10033.20023.30013.40013.50013.60003.70003.80003.9000

Mean μ = 250 gallons Standard deviation σ = 125 gallons Cost (c) = $10 per gallon Selling price (p)…

Answered: Goop Inc needs to order a raw material…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Goop Inc needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be Normally distributed with a mean of 250 gallons and a standard deviation of 125 gallons. Goop sells the polymer for $25 per gallon. Goop’s purchases raw material for $10 per gallon and Goop must spend $5 per gallon to dispose of all unused raw material due to government regulations. If demand is more than Goop can make, then Goop sells only what they made and the rest of demand is lost.

Suppose Goop wants to ensure that there is a 92% probability that they will be able to satisfy the customer's entire demand. How many gallons of the raw material should they purchase? *Use Table in image and round your answer to the nearest integer.

-4.0
-3.9
-3.8
-3.7
-3.6
-3.5
-3.4
-3.3
-3.2
-3.1
-3.0
-2.9
-2.8
-2.7
-2.6
-2.5
-2.4
-2.3
-2.2
-2.1
-2.0
-19
-1.8
-1.7
-1.6
-15
-1.4
-1.3
-12
-1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
1
2
3
4
5
6
7
8
9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
F)
0000
0000
0001
0001
0002
0002
0003
.0005
0007
0010
0013
0019
0026
0035
0047
0062
0082
0107
0139
0179
0228
0287
0359
0446
0548
0668
0808
0968
1151
1357
1587
1841
2119
2420
2743
3085
3446
3821
4207
4602
5000
5398
5793
.6179
6554
6915
7257
.7580
7881
8159
.8413
8643
8849
9032
9192
9332
9452
9554
9641
9713
9772
9821
9861
9893
9918
9938
9953
9965
.9974
9981
9987
9990
9993
9995
9997
9998
9998
9999
9999
1.0000
4
0000
0000
0000
0000
0000
0001
0001
0001
0002
0003
0004
0005
0008
0011
0015
0020
0027
0037
0049
0065
0085
0111
0143
0183
0232
0293
0367
0455
0561
0686
0833
1004
1202
1429
1687
1978
2304
2668
3069
3509
3989
4509
5069
5668
6304
6978
7687
8429
9202
1.0004
10833
11686
1.2561
1.3455
1.4367
1.5293
1.6232
1.7183
1.8143
1.9111
2.0085
2.1065
2.2049
2.3037
2.4027
2.5020
2.6015
2.7011
2.8008
2.9005
3.0004
3.1003
3.2002
3.3001
3.4001
3.5001
3.6000
3.7000
3.8000
3.9000

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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