Question: Grubby Stakes Mining Company is establishing a production plan for the current week at its Bonstock Lode, which has three main veins of varying characteristics. The net yields per ton for each of the veins is provided below.

Gold presently sells for $150 per ounce, silver sells for $5 per ounce, and copper sells for $2 per pound. Eastern is the most accessible vein, requiring I worker-hour per ton of ore; Northern and Tom's Lucky veins are more remote and require 2 worker-hours per ton. Only 300 worker-hours are available, and all labor costs are fixed. At least 100 tons must be mined from the Northern vein this week, so that it can be reshored next week; there are no tonnage limitations for the other tunnels. The company must also yield at least 5,000 pounds of copper to meet contractual commitments.

(a) Formulate Grubby's linear program to determine how many tons must be mined from

each vein to maximize total revenue.

(b) Find the optimal solution.