Monsanto sells genetically modified seed to farmers. It needs to decide how much seed to put into a warehouse to serve demand for the next growing season. It will make one quantity decision. It costs Monsanto $8 to make each kilogram (kg) of seed. It sells each kg for $45. If it has more seed than demanded by the local farmers, the remaining seed is sent overseas. Unfortunately, it only earns $3 per kg from the overseas market (but this is better than destroying the seed because it cannot be stored until next year). If demand exceeds its quantity, then the sales are lost—the farmers go to another supplier. As a forecast for demand, it will use a normal distribution with a mean of 300,000 and a standard deviation of 100,000. Round your answer to 2 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers. Use excel for accurate numbers. Don't round until the end. Monsanto’s maximum profit for this seed is $[xa]. The underage cost is $[xb]. The overage cost is $[xc]. The critical ratio is [xd]. Monsanto should place [xe] kg of seed in the warehouse before the growing season to maximize its expected profit. In such case, the expected leftover inventory will be [xf] kg, the expected sales will be [xg] kg, the expected profit will be $[xh], and the mismatch cost will be $[xi] (use the standard normal table below). If Monsanto puts 400,000 kg in the warehouse, its expected revenue (include both domestic revenue and overseas revenue) will be $[xj] (use the standard normal table below). Monsanto should place [xk] kg of seed in the warehouse if it wants to minimize its inventory while ensuring that the stockout probability is no greater than 10%

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ISBN:9781337406659
Author:WINSTON, Wayne L.
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Chapter2: Introduction To Spreadsheet Modeling
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Monsanto sells genetically modified seed to farmers. It needs to decide how much seed to put into a warehouse to serve demand for the next growing season. It will make one quantity decision. It costs Monsanto $8 to make each kilogram (kg) of seed. It sells each kg for $45. If it has more seed than demanded by the local farmers, the remaining seed is sent overseas. Unfortunately, it only earns $3 per kg from the overseas market (but this is better than destroying the seed because it cannot be stored until next year). If demand exceeds its quantity, then the sales are lost—the farmers go to another supplier. As a forecast for demand, it will use a normal distribution with a mean of 300,000 and a standard deviation of 100,000.

Round your answer to 2 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers. Use excel for accurate numbers. Don't round until the end.

Monsanto’s maximum profit for this seed is $[xa].

The underage cost is $[xb]. The overage cost is $[xc]. The critical ratio is [xd]. Monsanto should place [xe] kg of seed in the warehouse before the growing season to maximize its expected profit. In such case, the expected leftover inventory will be [xf] kg, the expected sales will be [xg] kg, the expected profit will be $[xh], and the mismatch cost will be $[xi] (use the standard normal table below).

If Monsanto puts 400,000 kg in the warehouse, its expected revenue (include both domestic revenue and overseas revenue) will be $[xj] (use the standard normal table below).

Monsanto should place [xk] kg of seed in the warehouse if it wants to minimize its inventory while ensuring that the stockout probability is no greater than 10% (use the standard normal table below).

-2.8
.0026
.0008
-0.1
.4602
.3509
2.6
.9953
2.6015
-2.7
.0035
.0011
.0
.5000
.3989
2.7
.9965
2.7011
-2.6
.0047
.0015
.1
.5398
.4509
2.8
.9974
2.8008
-2.5
.0062
.0020
.2
.5793
.5069
2.9
.9981
2.9005
-2.4
.0082
.0027
.3
.6179
.5668
3.0
.9987
3.0004
-2.3
.0107
.0037
.4
.6554
.6304
3.1
.9990
3.1003
-2.2
.0139
.0049
.5
.6915
.6978
3.2
.9993
3.2002
-2.1
.0 179
.0065
.6
.7257
.7687
3.3
.9995
3.3001
-2.0
.0228
.0085
.7
.7580
.8429
3.4
.9997
3.4001
-1.9
.0287
.0111
.8
7881
.9202
3.5
.9998
3.5001
-1.8
.0359
.0143
.9
.8159
1.0004
3.6
.9998
3.6000
-1.7
.0446
.0183
1.0
.8413
1.0833
3.7
.9999
3.7000
-1.6
.0548
.0232
1.1
.8643
1.1686
3.8
.9999
3.8000
-1.5
.0668
.0293
1.2
.8849
1.2561
3.9
1.0000
3.9000
-1.4
.0808
.0367
1.3
.9032
1.3455
4.0
1.0000
4.0000
Transcribed Image Text:-2.8 .0026 .0008 -0.1 .4602 .3509 2.6 .9953 2.6015 -2.7 .0035 .0011 .0 .5000 .3989 2.7 .9965 2.7011 -2.6 .0047 .0015 .1 .5398 .4509 2.8 .9974 2.8008 -2.5 .0062 .0020 .2 .5793 .5069 2.9 .9981 2.9005 -2.4 .0082 .0027 .3 .6179 .5668 3.0 .9987 3.0004 -2.3 .0107 .0037 .4 .6554 .6304 3.1 .9990 3.1003 -2.2 .0139 .0049 .5 .6915 .6978 3.2 .9993 3.2002 -2.1 .0 179 .0065 .6 .7257 .7687 3.3 .9995 3.3001 -2.0 .0228 .0085 .7 .7580 .8429 3.4 .9997 3.4001 -1.9 .0287 .0111 .8 7881 .9202 3.5 .9998 3.5001 -1.8 .0359 .0143 .9 .8159 1.0004 3.6 .9998 3.6000 -1.7 .0446 .0183 1.0 .8413 1.0833 3.7 .9999 3.7000 -1.6 .0548 .0232 1.1 .8643 1.1686 3.8 .9999 3.8000 -1.5 .0668 .0293 1.2 .8849 1.2561 3.9 1.0000 3.9000 -1.4 .0808 .0367 1.3 .9032 1.3455 4.0 1.0000 4.0000
F(z)
(z)
F(z)
I(z)
F(z)
I(z)
-4.0
.0000
.0000
-1.3
.0968
.0455
1.4
.9192
1.4367
-3.9
.0000
.0000
-1.2
.1151
.0561
1.5
.9332
1.5293
-3.8
.0001
.0000
-1.1
.1357
.0686
1.6
.9452
1.6232
-3.7
.0001
.0000
-1.0
.1587
.0833
1.7
.9554
1.7183
-3.6
.0002
.0000
-0.9
.1841
.1004
1.8
.9641
1.8143
-3.5
.0002
.0001
-0.8
2119
.1202
1.9
.9713
1.9111
-3.4
.0003
.0001
-0.7
2420
.1429
2.0
.9772
2.0085
-3.3
.0005
.0001
--0.6
2743
.1687
2.1
.9821
2.1065
-3.2
.0007
.0002
--0.5
.3085
.1978
2.2
.9861
2.2049
-3.1
.0010
.0003
-0.4
.3446
.2304
2.3
.9893
2.3037
-3.0
.0013
.0004
-0.3
.3821
.2668
2.4
.9918
2.4027
-2.9
.0019
.0005
-0.2
.4207
.3069
2.5
.9938
2.5020
-2.8
.0026
.0008
-0.1
4602
.3509
2.6
.9953
2.6015
Transcribed Image Text:F(z) (z) F(z) I(z) F(z) I(z) -4.0 .0000 .0000 -1.3 .0968 .0455 1.4 .9192 1.4367 -3.9 .0000 .0000 -1.2 .1151 .0561 1.5 .9332 1.5293 -3.8 .0001 .0000 -1.1 .1357 .0686 1.6 .9452 1.6232 -3.7 .0001 .0000 -1.0 .1587 .0833 1.7 .9554 1.7183 -3.6 .0002 .0000 -0.9 .1841 .1004 1.8 .9641 1.8143 -3.5 .0002 .0001 -0.8 2119 .1202 1.9 .9713 1.9111 -3.4 .0003 .0001 -0.7 2420 .1429 2.0 .9772 2.0085 -3.3 .0005 .0001 --0.6 2743 .1687 2.1 .9821 2.1065 -3.2 .0007 .0002 --0.5 .3085 .1978 2.2 .9861 2.2049 -3.1 .0010 .0003 -0.4 .3446 .2304 2.3 .9893 2.3037 -3.0 .0013 .0004 -0.3 .3821 .2668 2.4 .9918 2.4027 -2.9 .0019 .0005 -0.2 .4207 .3069 2.5 .9938 2.5020 -2.8 .0026 .0008 -0.1 4602 .3509 2.6 .9953 2.6015
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