1-Blacktop Reﬁning extracts minerals from ore mined at two different sites in Mon-

tana. Each ton of ore type 1 contains 20% copper, 20% zinc and 15% magnesium.

Each ton of ore type 2 contains 30% copper, 25% zinc and 10% magnesium. Ore type

1 costs $90 per ton, while ore type 2 costs $120 per ton. Blacktop would like to buy

enough ore to extract at least 8 tons of copper, 6 tons of zinc, and 5 tons of magne-

sium in the least costly manner.

a. Formulate an LP model for this problem.

b. Sketch the feasible region for this problem.

c. Find the optimal solution.

2-PC-Express is a computer retail store that sells desktops and laptops. The company

earns $600 on each desktop computer it sells and $900 on each laptop. The computers

PC-Express sells are actually manufactured by another company. This manufacturer

has a special order to ﬁll for another customer and cannot ship more than 80 desktops

and 75 laptops to PC-Express next month. The employees at PC-Epress must spend about 2 hours installing software and checking each desktop computer they sell.They spend roughly 3 hours to complete this process for laptop computers. They expect to have about 300 hours available for this purpose during the next month. The store’s management is fairly certain that they can sell all the computers they order but are unsure how many desktops and laptops they should order to maximize profits.

a. Formulate an LP model for this problem.

b. Sketch the feasible region for this problem.

c. Find the optimal solution to the problem by enumerating the corner points