A gold processor has three mines of gold ore, mine A, mine B, and mine C. In order to keep his plant running, at least 200 tons of ore must be processed each day. Ore from mine A costs $200 per ton to process, ore from mine B costs $100 per ton to process, and ore from mine C costs $150 per ton to process Moreover, Federal Regulations require that the amount of ore processed from one mine cannot exceed twice the amount of ore processed from any other mine.
Ore from mine A yields 2 oz. of gold per ton, ore from mine B yields 3 oz. of gold per ton, and ore from mine C yields 2.5 oz. of gold per ton. Because of the purity of the gold from each mine, each one yields a different price. Mine A yields $450 per oz, mine B yields $380 per oz, and mine C yields $420 per oz.
Historical data shows that the maximum yield of ore from mine A is 120 tons per day, mine B is 150 tons per day and mine C is 80 tons per day. The maximum number of workers the can work mine A is 55, mine B is 70, and mine C is 40. The capacity of each mine is proportional to the maximum number of workers working that mine. For example if mine B has 70 workers, it can operate at 100% capacity and produce 150 tons per day, if it has 35 workers it is operating at 50% capacity and can produce 75 tons per day. The capacity of each mine is required to operate at least above 70%.
There are also ratio requirements for worker to trucks and jack hammers for each mine.
For every 10 workers at each mine, there must be at least one truck and for every 5 workers at each mine there must be at least 1 jackhammer. The company has 135 workers, 14 trucks, and 30 jackhammers, not all workers, trucks and jackhammers have to be assigned. Each worker costs the company $500 per day, each truck costs the company $2,800 per day to operate and each jackhammer costs the company $300 per day. Total costs must be kept to less than $150,000 per day, including labor, equipment and processing costs.
How many workers, trucks, and jack hammers should be assigned to each mine in order to maximize profit? What will be the maximum profit? What will be the cost and revenue? Assume the decision variables can be fractional values.
1. Formulate a linear programming model for this problem by:
A. Listing and labeling all of the decision variables.
B. Creating an objective function for the model.
C. List all of the constraints for the model.