Question: Formulate and solve linear programming model

Carrie sells food at each basketball game (a total of 6 games). It costs her $1,000 per game for booth fees. She has to rent an oven to keep food warm $600 for all six games.

Costs are $6 for each 14 inch pizza with eight slices, $0.45 for each hot dog, and $0.90 for each sandwich. Carrie plans to sell each slice of pizza and hot dog for $1.50 and $2.25 for each sandwich.

The oven has 16 shelves, each with 3ft by 4ft. She plans to fill the oven before game starts and again at half time. A hot dog takes up 16 square feet, a sandwich 25 square feet, and 14 inch cheese pizzas. She plans to fill up oven twice throughout each game.

She expects to sell at least as many slices of pizza as hot dogs and sandwiches combined. She also anticipates selling at least twice as many hot dogs as sandwiches.

Carrie needs to clear at least $1000 profit for each game after expenses.

(a) Formulate and solve a linear programming model for Carrie that will help advise her about renting booth.

(b) If Carrie borrowed money from a friend before first game to increase ingredients could she increase her profit?

(c) Could Carrie afford to hire a friend for $100 per game to help her?