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 c

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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".

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