3. Copperfield Mining Companyownstwo mines, each of which produces three grades of ore high, medium, andlow. Thecompany has a contract to supply a smelting company with at least 150tons ofhigh-grade ore, 120 tons of medium-grade ore, and 150 tons of low-gradeore.Each mine produces a certain amount of each type of ore during each hourthat itoperates. Mine 1 produces 6.5 tons of high-grade ore, 3.2 tons ofmedium-gradeore, and 4.8 tons of low grade ore per hour. Mine 2 produces 3.2,4.0, and 9.8tons, respectively, of high-, medium-, and low-grade ore per hour.It costsCopperfield $400 per hour to operate mine 1, and it costs $280 per hourtooperate mine 2. The company wants to determine the number of hours it needstooperate each mine so that its contractual obligations can be met at thelowestcost.

Formulate a linear programmingmodel for this problem.

Note: Do NOT solve the modelafter formulating.

4. Determine whether thefollowinglinear programming problem is infeasible, unbounded, or has multipleoptimalsolutions. Draw a graph and explain your conclusion.

Maximize 80x + 60y

Subjectto

-3x + 4y< 60

2x + 3y> 60

2x + y >40

x, y 0