A manufacturer of textile dyes can use two different processing routings for a particular type of dye. Routing 1 uses drying press A, and routing 2 uses drying press B. Roth routings require the same mixing vat to blend chemicals for the dye before drying. The following table shows the time requirements and capacities of these processes:

Each kilogram of dye processed on routing issues 20 liters of chemicals, whereas each kilogram of dye processed on routing 2 uses only 15 liters. The difference results from differing yield rates of the drying presses. Consequently the profit per kilogram processed on routing 1 is $50 and on routing 2 is $65. A total of 450 liters of input chemicals is available.
a. The constraints and objective function to maximize profits.
b. Use the graphic method of linear programming to find the optimal solution.
c. Identify any constraints with slack orsurplus.

Time Requirements (hr/kg) Process Routing1 Routing 2 Capacity (hr) Mixing Dryer A 54 120 180