A coal company owns mines in two different locations. Each day, mine 1 produces 4 tons of anthracite (hard) coal, 4 tons of ordinary coal, and 7 tons of bituminous (soft) coal. Each day, mine 2 produces 10 tons of anthracite, 5 tons of ordinary coal, and 5 tons of bituminous coal. It costs the company $150 per day to operate mine 1 and $200 per day to operate mine 2. An order is received for 80 tons of anthracite, 60 tons of ordinary coal, and 75 tons of bituminous coal.
(a) Fill in the following chart:

(b) Let x be the number of days that mine 1 should be operated and y the number of days that mine 2 should be operated. Refer to the chart, and give three inequalities that x and y must satisfy to fill the order.
(c) Give other requirements that x and y must satisfy.
(d) Find the total cost of operating mine 1 for x days and mine 2 for y days.
(e) Graph the feasible set for the mining problem.

Transcribed Image Text:

Mine 2 | Ordered Mine 1 Anthracite Ordinary Bituminous Daily cost