Kellpost Cereal Company sells four products: (1) Special L (a low-calorie, high-nutrition cereal); (2) Corn Bran (another low-calorie, high-nutrition cereal); (3) Admiral Smacks (a sugary cereal pitched at the children's market); and (4) Honey Pops (another sweet cereal pitched at the children's market). Kellpost has sufficient production capacity to produce a total of 10,000 boxes of cereal per month. For each of the past 16 months, Kellpost has kept track of the price and sales of each product. (These data are listed in the file P07_72.xlsx.) Market executives believe that Special L and Corn Bran might be substitutes for each other, as might be Admiral Smacks and Honey Pops. For example, this means that an increase in the price of Special L might raise the sales of Corn Bran. The variable cost of bringing a box of each cereal to market is as follows: Special L, $2.00; Corn Bran, $2.20; Admiral Smacks, $2.30; Honey Pops, $2.40. a.  Use the given information to determine the price for each cereal that will enable Kellpost to maximize profits. If needed, round your answers to two decimal digits.   b.  Now suppose that Kellpost can increase its monthly production capacity. The cost (per year) of doing this is $20,000 per 1000 boxes of added monthly capacity. Can you determine an optimal capacity level? If an answer is zero, enter "0

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter13: Regression And Forecasting Models
Section: Chapter Questions
Problem 42P: The file P13_42.xlsx contains monthly data on consumer revolving credit (in millions of dollars)...
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Kellpost Cereal Company sells four products: (1) Special L (a low-calorie, high-nutrition cereal); (2) Corn Bran (another low-calorie, high-nutrition cereal); (3) Admiral Smacks (a sugary cereal pitched at the children's market); and (4) Honey Pops (another sweet cereal pitched at the children's market). Kellpost has sufficient production capacity to produce a total of 10,000 boxes of cereal per month. For each of the past 16 months, Kellpost has kept track of the price and sales of each product. (These data are listed in the file P07_72.xlsx.) Market executives believe that Special L and Corn Bran might be substitutes for each other, as might be Admiral Smacks and Honey Pops. For example, this means that an increase in the price of Special L might raise the sales of Corn Bran. The variable cost of bringing a box of each cereal to market is as follows: Special L, $2.00; Corn Bran, $2.20; Admiral Smacks, $2.30; Honey Pops, $2.40.

a.  Use the given information to determine the price for each cereal that will enable Kellpost to maximize profits. If needed, round your answers to two decimal digits.

 

b.  Now suppose that Kellpost can increase its monthly production capacity. The cost (per year) of doing this is $20,000 per 1000 boxes of added monthly capacity. Can you determine an optimal capacity level? If an answer is zero, enter "0".

A
B
D
E
F
H
K
1 Cereal datal
2
3 Historical data
4
Prices
Sales
Special L
Admiral Smacks
Honey Pops
Honey Pops
$4.35
5
Month
Corn Bran
Admiral Smacks
Special L
Corn Bran
6
1
$4.20
$4.10
$4.22
3251
4933
3463
5467
7
2
$3.90
$4.30
$4.12
$4.18
3524
4629
3471
5607
8
3
$4.10
$4.50
$4.32
$4.22
3349
4456
3362
5494
9
4
$4.00
$4.40
$3.86
$4.13
3380
4497
3875
5507
10
$3.80
$3.80
$3.99
$4.56
3447
5193
3726
5084
11
$3.90
$3.90
$3.76
$3.78
3560
4885
3961
6063
12
7
$3.80
$3.70
$4.07
$3.89
3689
5344
3669
5953
13
8.
$4.30
$3.60
$4.05
$3.97
3013
5522
3654
5959
14
$3.60
$3.95
$4.09
$4.22
3824
4935
3720
5470
15
10
$3.50
$4.06
$4.12
$4.13
3760
4845
3641
5659
16
11
$3.40
$4.12
$4.13
$4.50
4047
4848
3655
5183
17
12
$3.70
$4.12
$5.16
$4.00
3746
4706
2430
6110
18
13
$3.80
$4.20
$4.17
$4.06
3722
4665
3614
5683
19
14
$3.90
$4.28
$4.00
$4.22
3461
4653
3652
5464
20
15
$4.00
$4.10
$3.90
$4.12
3322
4847
3881
5660
21
16
$4.10
$3.90
$3.96
$3.94
3320
5090
3751
5932
22
23
24
25
Transcribed Image Text:A B D E F H K 1 Cereal datal 2 3 Historical data 4 Prices Sales Special L Admiral Smacks Honey Pops Honey Pops $4.35 5 Month Corn Bran Admiral Smacks Special L Corn Bran 6 1 $4.20 $4.10 $4.22 3251 4933 3463 5467 7 2 $3.90 $4.30 $4.12 $4.18 3524 4629 3471 5607 8 3 $4.10 $4.50 $4.32 $4.22 3349 4456 3362 5494 9 4 $4.00 $4.40 $3.86 $4.13 3380 4497 3875 5507 10 $3.80 $3.80 $3.99 $4.56 3447 5193 3726 5084 11 $3.90 $3.90 $3.76 $3.78 3560 4885 3961 6063 12 7 $3.80 $3.70 $4.07 $3.89 3689 5344 3669 5953 13 8. $4.30 $3.60 $4.05 $3.97 3013 5522 3654 5959 14 $3.60 $3.95 $4.09 $4.22 3824 4935 3720 5470 15 10 $3.50 $4.06 $4.12 $4.13 3760 4845 3641 5659 16 11 $3.40 $4.12 $4.13 $4.50 4047 4848 3655 5183 17 12 $3.70 $4.12 $5.16 $4.00 3746 4706 2430 6110 18 13 $3.80 $4.20 $4.17 $4.06 3722 4665 3614 5683 19 14 $3.90 $4.28 $4.00 $4.22 3461 4653 3652 5464 20 15 $4.00 $4.10 $3.90 $4.12 3322 4847 3881 5660 21 16 $4.10 $3.90 $3.96 $3.94 3320 5090 3751 5932 22 23 24 25
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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,