Product pricing and profit analysis with bottleneck operations

Hercules Steel Company produces three grades of steel: high, good, and regular grade. Each of these products $($grades$)$ has high demand in the market, and Hercules is able to sell as much as it can produce of all three. The furnace operation is a bottleneck in the process and is running at $100\%$ of capacity. Hercules wants to improve steel operation profitability. The variable conversion cost is $$15$ per process hour. The fixed cost is $$200,000.$ In addition, the cost analyst was able to determine the following information about the three products:

$\backslash$table$[[,\backslash$table$[[$High$],[$Grade$]],\backslash$table$[[$Good$],[$Grade$]],\backslash$table$[[$Regular$],[$Grade$]]],[$Budgeted units produced,$5,000,5,000,5,000],[$Total process hours per unit,$12,11,10],[$Furnace hours per unit,$4,3,2\mathrm{.}5],[$Unit selling price,$$280,$$$270,$$$250$