Formulate linear programming model

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Reference no: EM132261465

Solve the following problem using POM/QM Software and state the answers clearly.

The Majan Company owns two mines, both of which produce three grades of ore— high, medium, and low. The company has a contract to supply a smelting company with at least 12 tons of high-grade ore, 8 tons of medium-grade ore, and 24 tons of low-grade ore. Each mine produces a certain amount of each type of ore each hour it is in operation. Mine 1 produces 6 tons of high-grade, 2 tons of medium-grade, and 4 tons of low-grade ore per hour. Mine 2 produces 2 tons of high-grade, 2 tons of medium-grade, and 12 tons of low-grade ore per hour. It costs OMR 200 per hour to mine each ton of ore from mine 1, and it costs OMR160 per hour to mine a ton of ore from mine 2. The company wants to determine the number of hours it needs to operate each mine so that contractual obligations can be met at the lowest cost.

Questions:

1. Formulate a linear programming model to determine the number of hours it needs to operate each mine.

2. Solve the model using the POM/QM Software and identify the amount of surplus production (i.e., the excess over the minimum requirements).

3. Determine the sensitivity ranges for the objective function coefficients and constraint quantity values.

4. Without solving the problem again, how would you ascertain what would be the effect on the optimal solution if the cost of mining for Mine 1 reduces from $200 to $150?

5. What would be the effect on the optimal solution if the demand for medium grade ore increased from 8to 18 tons?

Reference no: EM132261465

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