A paint supplier has two machines that produce both indoor paint and outdoor paint. To meet one of its contractual obligations, the company must produce at least 60 gal of indoor paint and 100 gal of outdoor paint. Machine I makes 3 gal of indoor paint and 10 gal of outdoor paint per hour. Machine II makes 4 gal of indoor paint and 5 gal of outdoor paint per hour. It costs $28 per hour to run machine I and $33 per hour to run machine II.

(a) List the constraints.

(b) Determine the objective function.

(c) Graph the set of constraints. 

(d) Determine the vertices of the feasible region.

(e) How many hours should each machine be operated to fulfill the contract at a minimum cost? 

(f)  Determine the minimum cost.