# Maximizing Profit in Ore Mining

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

A mine owner has the right to extract ore for a time duration . Initially there is ore in the ground. As ore is extracted, the instantaneous stock of ore declines, and is the extraction rate. Assume that the ore sells at a constant price and the extraction cost is .

[more]

This Demonstration finds the optimal extraction rate that maximizes the profit (or performance measure), defined as .

When you set the value of the parameters , , and , the Demonstration plots the rate of extraction , the instantaneous stock of ore , and the costate (also called shadow price) . Assume that the ore remaining in the ground at time has no value (i.e. there is no "scrap value", or ).

Two solution methods are adopted: (1) the discrete-time method (solutions indicated by the blue triangles), and (2) the continuous-time method (the red curves).

You can readily check that when the duration is decreased, the extraction rate is larger. Also for a fixed value of , if you increase the initial stock of ore in the mine, then both the profit and the extraction rate are larger. The values of for the discrete-time and continuous-time versions are indicated in blue and red, respectively. The two values show very close agreement. Finally, you can lower the ore price, which results in a lower profit.

[less]

Contributed by: Housam Binous and Ahmed Bellagi (January 2016)
(King Fahd University of Petroleum & Minerals, KSA; University of Monastir, Tunisia)
Open content licensed under CC BY-NC-SA

## Details

Reference

[1] Wikipedia. "Optimal control." (Jan 25, 2016) en.wikipedia.org/wiki/Optimal_control.

## Permanent Citation

Housam Binous and Ahmed Bellagi

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send