Happy Dog Inc. produces three types of dog food. Puppy Blend is produced for dogs that are less than a year old, Adult Blend for dogs between 1 and 8 years old, and Geriatric Blend for dogs older than 8 years. Each blend, sold in 5 pound bags, has a unique recipe that requires, among other ingredients, exact quantities of certain raw materials. Chicken Fish Meal Soy Flour Demand (in5 lb. bags) Puppy Blend Adult Blend Geriatric Blend Availability of rawmaterial 2.5 lbs. 1.5 lbs. 1.0 lbs. 10,000 lbs. 1.0 lbs. 2.0 lbs. 2.0 lbs. 20,000 lbs. 0.5 lbs. 0.5 lbs. 1.0 lbs. 5,000 lbs. 2000 8000 1000 a. Formulate a linear programming model that produces as many bags of dog food as possible without exceeding the demand or the available supply of raw material.b. Reformulate the linear programming model if the company is now interested in maximizing their profit 1price - raw material cost2 from dog food production. Assume that Puppy Blend sells for $9.50 per bag, Adult Blend sells for $8.50 per bag, and Geriatric Blend sells for $9.00 per bag. Further, Chicken costs $2.50 per pound Fish Meal costs $1.25 per pound, and Soy Flour costs $2.00 per pound. How does this new information change your linear programming model?
Happy Dog Inc. produces three types of dog food. Puppy Blend is produced for dogs that are less than a year old, Adult Blend for dogs between 1 and 8 years old, and Geriatric Blend for dogs older than 8 years. Each blend, sold in 5 pound bags, has a unique recipe that requires, among other ingredients, exact quantities of certain raw materials.
| Chicken | Fish Meal | Soy Flour | Demand (in 5 lb. bags) |
|
|
Puppy Blend Adult Blend Geriatric Blend Availability of raw |
2.5 lbs. 1.5 lbs. 1.0 lbs. 10,000 lbs. |
1.0 lbs. 2.0 lbs. 2.0 lbs. 20,000 lbs. |
0.5 lbs. 0.5 lbs. 1.0 lbs. 5,000 lbs. |
2000 8000 1000
|
a. Formulate a linear programming model that produces as many bags of dog food as possible without exceeding the demand or the available supply of raw material.
b. Reformulate the linear programming model if the company is now interested in maximizing their profit 1price - raw material cost2 from dog food production. Assume that Puppy Blend sells for $9.50 per bag, Adult Blend sells for $8.50 per bag, and Geriatric Blend sells for $9.00 per bag. Further, Chicken costs $2.50 per pound Fish Meal costs $1.25 per pound, and Soy Flour costs $2.00 per pound. How does this new information change your linear programming model?
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