lating a Linear Programming Model 1. Happy Dog Inc. pro Blend is produced Adult Blend ford Geriatric Blend for sold in 5-pound be among other ingre materials. Inc. produces three types of dog food. Puppy produced for dogs that are less than a year old, Blend for dogs between 1 and 8 years old, and Blend for dogs older than 8 years. Each blend, 5-pound bags, has a unique recipe that requires, other ingredients, exact quantities of certain raw Chicken Demand (in 5-lb. bags) 2,000 Puppy Blend 8,000 Fish Meal Soy Flour 1.0 lbs. 0.5 lbs. 2.0 lbs. 0.5 lbs. 2.0 lbs. 1.0 lbs. 20,000 lbs. 5,000 lbs. 2.5 lbs. 1.5 lbs. 1.0 lbs. 10,000 lbs. Adult Blend Geriatric Blend Availability of raw material 1,000 a. Formulate a linear programming model that pro- duces 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 produc- tion. 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