(3) Dorian Auto is considering manufacturing three types of autos: compact, midsize, and large. The resources required for, and the profits yielded by, each type of car are in the next table: Auto type Steel required Labor required Profit yielded Compact Midsize 1.5 tons 3 tons 30 hours 25 hours $2,000 $3,000 Large 5 tons 40 hours $4,000 At present, 6,000 tons of steel and 60,000 hours of labor are available. For production of a type of car to be economically feasible, at least 1,000 cars of that type must be produced. Formulate an IP to maximize Dorian's profit. (Hint: Define decision variables to be the numbers of each type of auto to be produced and use either-or constraints to account for either situation when a certain type of auto is produced and when it is not produced.)