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.

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 (price - raw material cost) 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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Demand (in 5-lb. bags) Fish Meal Chicken Soy Flour Puppy Blend 0.5 lbs. 2.5 lbs. 1.0 lbs. 2,000 8,000 Adult Blend 1.5 lbs. 2.0 lbs. 0.5 lbs. 2.0 lbs. 1,000 Geriatric Blend 1.0 lbs. 1.0 Ibs. 20,000 lbs. Availability of raw material 10,000 lbs. 5,000 lbs.