Philips machinery is trying to determine its product mix for next year. It produces two products, a mixer and a blender. Philips makes about $80 profit on each mixer and $60 on each blender. Philips factory capacity is limited by labor, materials and machinery. Only 150,000 hours of labor are available next year, and each mixer uses 10hours and each blender uses 5hours. Only 300,000 pounds of steel are available next year, and each mixer uses 10pounds and each blender uses 15pounds. Only 190,000 machine hours are available next year, and each mixer uses 5hours and each blender uses 4 hours.

a. Formulate the objective function and the constraint function for Philips machinery. Determine the decision variables.

b. Solve Philips machinery simultaneously and graphically. What is the optimal solution?

c. How many mixers and blenders should Philip include in its business plan for next year? d. How much profit will result?