Question

universal mines inc. operates three mines in west virginia. the ore from each mine is separated into two grades before it is shipped. the daily production capacities of the three mines, as well as their daily operating costs, are as follows: high-grade ore, tons/day low-grade ore, tons/day operating cost in $/day mine i 4 4 20,000 mine ii 6 4 22,000 mine iii 1 6 18,000 universal has committed itself to deliver 54 tons of high-grade order and 65 tons of low-grade ore by the end of the week. universal can run its mines seven days a week if required. determine the number of days each mine should be operated during the upcoming week if universal mines is to fulfill its commitment at the minimum total cost. round the answers to two decimal places. a. the number of days mine i should operate

Answer 1

To determine the optimal number of days each mine should operate, we can use linear programming to solve for the minimum total cost while fulfilling Universal Mines' commitment.

Step-by-step explanation:

To determine the number of days each mine should operate, we need to find the optimal solution that fulfills Universal Mines' commitment at the minimum total cost. Let's use linear programming to solve this problem.

Let xi be the number of days Mine i should operate, where i ranges from 1 to 3.

Minimize the total cost: 20,000x1 + 22,000x2 + 18,000x3

Subject to the following constraints:

4x1 + 6x2 + x3 ≥ 54 (for high-grade ore)

4x1 + 4x2 + 6x3 ≥ 65 (for low-grade ore)

x1, x2, x3 ≥ 0 (since the number of days cannot be negative)

By solving this linear programming problem, we can find the optimal number of days each mine should operate to fulfill the commitment at the minimum total cost.