2. Inspired by the magnificent cats owned by your professor, you and your friends decide to...

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2. Inspired by the magnificent cats owned by your professor, you and your friends decide to open a kitten shelter for rescued cats. Since optimization is your absolute favorite course, you and your friends decide to plan the operations of the shelter using a linear model. There are n rescued kittens in the shelter. Each one requires at least 1 pound of food and 2 pounds of litter every month. There are four local suppliers for cat food and litter. Table 1 shows their prices and capacities: Cost per pound of Cost per pound of Total food available per Total litter available per food litter month month Supplier 1 f1 11 F1 L1 Supplier 2 f2 12 F2 L2 Supplier 3 f3 13 F3 L3 Supplier 4 f4 14 F4 L4 After negotiating with Supplier 1, they agree to give you a special discount as long as the amount of food you buy from them is at least 50% of the amount of food you buy from all the other suppliers combined. The discounted price is already reflected by f1, and your model has to enforce the agreement reached. Your goal is to operate the shelter at minimum cost. Formulate the problem as a linear program by following these steps: a. Precisely define decision variables for the model b. State the objective function c. State the constraints 2. Inspired by the magnificent cats owned by your professor, you and your friends decide to open a kitten shelter for rescued cats. Since optimization is your absolute favorite course, you and your friends decide to plan the operations of the shelter using a linear model. There are n rescued kittens in the shelter. Each one requires at least 1 pound of food and 2 pounds of litter every month. There are four local suppliers for cat food and litter. Table 1 shows their prices and capacities: Cost per pound of Cost per pound of Total food available per Total litter available per food litter month month Supplier 1 f1 11 F1 L1 Supplier 2 f2 12 F2 L2 Supplier 3 f3 13 F3 L3 Supplier 4 f4 14 F4 L4 After negotiating with Supplier 1, they agree to give you a special discount as long as the amount of food you buy from them is at least 50% of the amount of food you buy from all the other suppliers combined. The discounted price is already reflected by f1, and your model has to enforce the agreement reached. Your goal is to operate the shelter at minimum cost. Formulate the problem as a linear program by following these steps: a. Precisely define decision variables for the model b. State the objective function c. State the constraints