A mining company exploits two types of minerals, its starting cost is $ 100,000. The cost per kg is $ 100 and $ 150 respectively. For safety, the overall maximum inventory should be 80,000 kg. Product 2 that requires a maximum inventory of $ 2,000,000 invested in warehouse. Consider that the monthly demand is 40,000 and 30,000 units respectively. The weekly cost of the inventory rate is 10% for the average inventory. The total inventory turnover policy must be greater than or equal to 50 (remember that inventory turnover is defined as the annual demand for all items expressed in dollars, divided by the average total inventory investment). Formulate the problem as a mathematical model that minimizes the total annual cost.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.EA: Extended Application Estimating Depletion Dates For Minerals
Problem 4EA
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A mining company exploits two types of minerals, its starting cost is $ 100,000. The cost per kg is $ 100 and $ 150 respectively. For safety, the overall maximum inventory should be 80,000 kg. Product 2 that requires a maximum inventory of $ 2,000,000 invested in warehouse. Consider that the monthly demand is 40,000 and 30,000 units respectively. The weekly cost of the inventory rate is 10% for the average inventory. The total inventory turnover policy must be greater than or equal to 50 (remember that inventory turnover is defined as the annual demand for all items expressed in dollars, divided by the average total inventory investment).

Formulate the problem as a mathematical model that minimizes the total annual cost.

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