Handcrafted Soap is a manufacturer of fine cosmetic soap products. Sweet Treats' two main products are soap and cleanser. Each batch of soap consumes 50 pounds of glycerin and 30 pounds of oil. Each batch of cleanse consumes 20 pounds of glycerin and 40 pounds of oil. Batches of soap and cleanser sell at retail for $300 and $250, respectively.

Handcrafted Soap can each week obtain up to 60 pounds of glycerin, at $0.5 per pound, and up to 30 pounds of oil, at $0.25 per pound.

Part 1: Formulate as a linear program the problem of finding the maximum profit weekly production mix.

Part 2: Solve the linear program from Part A using the Simplex method.

Part 3: Use a graphical approach to verify that your answer from Part B is correct.

Part 4: The company would like to ensure that at least 0.5 batches of cleanser are sold each week, on average. Take this desire into account in formulating as a linear program the problem of finding the maximum profit weekly production mix.

Part 5: Use the Big-M method with at least one artificial variable to solve your model from Part 4.