Chapter 8. In Problem Set 6, we worked on a problem for Flor’s Flours, a small business that produces two types of ready-to-use multigrain flours using organic products such as bulgur wheat, garbanzos, and jasmine rice and sells them at a Farmer’s Market every weekend. The first blend is called Pancake-Me and is priced at $6.50 per lb. and the second blend is called the Bake-Me and is priced at $4.50 per lb. These healthier versions of the traditional flour used for cooking and baking are fairly popular and Flor realizes that she needs to have a more formalized method of how to blend the flours if she hopes to minimize her costs and maximize her profits by continuing to sell the flours on a larger scale. The costs of obtaining the components – bulgur wheat, garbanzos, and jasmine rice are different. After running the original model, Flor found that she had more Jasmine rice left on hand than she really needed and made the following changes to her blends and bulk-grain purchases. With a lot of painstaking trial-and-error, Flor updated some of the following guidelines to minimize any wasted product: Pancake-Me Blend should have: At least 50% wheat At least 20% garbanzos At least 20% jasmine rice Bake-Me Blend should have: At the most 60% wheat At least 25% garbanzos At the most 10% jasmine rice Moreover, Flor now purchases 175 lbs. of bulgur wheat at $1.25 per lb., 125 lbs. of garbanzos at $0.87 per lb. and 40 lbs. of rice at $1.79 per lb. for the next month’s production by ordering whole grains in bulk on the internet. She still needs to have at least 100 pounds of the Bake-Me blend available to cover the next month’s demand at the Farmer’s Market. Based on this NEW information, answer the following questions: Flor’s new profit for the month would be $________ (round to two decimal places) Fill in the following table to show how much of each component Flor should use for each blend and what her total monthly production of each flour is (you can write whole numbers): Component Wheat Garbanzo Rice TOTAL Pancake-Me ________ ________ _______ _______ Bake-Me _________ ________ _______ _______ TOTAL ________ _______ _______
Chapter 8. In Problem Set 6, we worked on a problem for Flor’s Flours, a small business that produces two types of ready-to-use multigrain flours using organic products such as bulgur wheat, garbanzos, and jasmine rice and sells them at a Farmer’s Market every weekend. The first blend is called Pancake-Me and is priced at $6.50 per lb. and the second blend is called the Bake-Me and is priced at $4.50 per lb. These healthier versions of the traditional flour used for cooking and baking are fairly popular and Flor realizes that she needs to have a more formalized method of how to blend the flours if she hopes to minimize her costs and maximize her profits by continuing to sell the flours on a larger scale. The costs of obtaining the components – bulgur wheat, garbanzos, and jasmine rice are different. After running the original model, Flor found that she had more Jasmine rice left on hand than she really needed and made the following changes to her blends and bulk-grain purchases.
With a lot of painstaking trial-and-error, Flor updated some of the following guidelines to minimize any wasted product:
Pancake-Me Blend should have:
- At least 50% wheat
- At least 20% garbanzos
- At least 20% jasmine rice
Bake-Me Blend should have:
- At the most 60% wheat
- At least 25% garbanzos
- At the most 10% jasmine rice
Moreover, Flor now purchases 175 lbs. of bulgur wheat at $1.25 per lb., 125 lbs. of garbanzos at $0.87 per lb. and 40 lbs. of rice at $1.79 per lb. for the next month’s production by ordering whole grains in bulk on the internet. She still needs to have at least 100 pounds of the Bake-Me blend available to cover the next month’s demand at the Farmer’s Market. Based on this NEW information, answer the following questions:
- Flor’s new profit for the month would be $________ (round to two decimal places)
- Fill in the following table to show how much of each component Flor should use for each blend and what her total monthly production of each flour is (you can write whole numbers):
|
Component |
||||
|
Wheat |
Garbanzo |
Rice |
TOTAL |
|
|
Pancake-Me |
________ |
________ |
_______ |
_______ |
|
Bake-Me |
_________ |
________ |
_______ |
_______ |
|
TOTAL |
________ |
_______ |
_______ |
|
From the given data:
Let the decision variables be as shown below (all in lbs):
| Wheat | Garbanzo | Rice | |
| Pancake-Me | X1 | X2 | X3 |
| Bake-Me | y1 | y2 | y3 |
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