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# Optimal Solution for Product Cost

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I'm looking to understand how to determine the optimization for the following problem.

Part One: What is the optimal solution for this problem?

M&D Chemicals produces two products that are sold as raw materials to companies manufacturing bath soaps and laundry detergents. Based on an analysis of current inventory levels and potential demand for the coming month, M&D's management has specified that the combined production for products A and B must total at least 350 gallons. Separately, a major customer's order for 125 gallons of product A must also be satisfied. Product A requires 2 hours of processing time per gallon while product B requires 1 hour of processing time per gallon, and for the coming month, 600 hours of processing time are available. M&D's objective is to satisfy these requirements at a minimum total production cost. Production costs are \$2 per gallon for product A and \$3 per gallon for product B.

Part Two:
Now assume that the cost per gallon for Product A is increased to \$3 per gallon.

What is the optimal solution for this problem?