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. Cereal Brands Unit Price Special L $ Corn Bran $ Admiral Smacks $ Honey Pops $ 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". Extra capacity (boxes): 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 7 $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 12 $3.70 $4.12 $5.16 $4.00 3746 4706 2430 6110 13 $3.80 $4.20 $4.17 $4.06 3722 4665 3614 5683 14 $3.90 $4.28 $4.00 $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
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. Cereal Brands Unit Price Special L $ Corn Bran $ Admiral Smacks $ Honey Pops $ 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". Extra capacity (boxes): 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 7 $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 12 $3.70 $4.12 $5.16 $4.00 3746 4706 2430 6110 13 $3.80 $4.20 $4.17 $4.06 3722 4665 3614 5683 14 $3.90 $4.28 $4.00 $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
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 73P
Related questions
Question
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.
| Cereal Brands | Unit Price | |
| Special L | $ | |
| Corn Bran | $ | |
| Admiral Smacks | $ | |
| Honey Pops | $ |
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".
Extra capacity (boxes):
| 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 |
| 7 | $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 |
| 12 | $3.70 | $4.12 | $5.16 | $4.00 | 3746 | 4706 | 2430 | 6110 |
| 13 | $3.80 | $4.20 | $4.17 | $4.06 | 3722 | 4665 | 3614 | 5683 |
| 14 | $3.90 | $4.28 | $4.00 | $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 |
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 6 images
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,