Reference no: EM132304664

LP Formulation

To make stuffed toys, you need fake-fur fabric, filling, and the eyes, plus time on a sewing machine. You currently are making three animals: a spider, an elephant, and a mouse (they all use grey fake-fur). The spider uses 2 square feet of fake fur, while the elephant uses 3 square feet and the mouse uses ½ square feet. The spider uses ¾ lb. of filling, the elephant uses 1.5 lbs. of filling and the mouse uses 1/10 lb. of filling. The spider has 8 eyes, while the elephant has 2 eyes and the mouse has only one eye (it is a pirate mouse). You have 400 square feet of grey fake fur, and your boss wants it used up on this production run. You have 500 lbs. of stuffing and 1,000 eyes. You can sell at least three times as many spiders as mice, and elephants must be no more than 40% of the total production. You make a profit of $2.00 on the spiders, of $3.50 on the elephants and $1.75 on the mice. The sewing machines are available 200 hour per week, and the spider needs 45 minutes, the elephant 20 minutes and the mouse 15 minutes. Provide the formulation for this problem, including the variable definitions, all constraints and the objective function.