The Carolina Chemical Company (CCC) makes two products, soap and shampoo, both in liquid form.The same two raw material inputs, glycerin and potash, and the same production line are used in the manufacture of each.Each production day, one ton of glycerin and two tons of potash are available.Each gallon of soap requires 8 pounds of glycerin and 32 pounds of potash, while a gallon of shampoo uses 12 pounds of glycerin and 19 pounds of potash.
CCC's production day is 8 full hours (480 minutes).Its production line can turn out 25 gallons of soap, or 20 gallons of shampoo, per hour.Only one product can be made at a time, but the line is easily changed over at negligible cost from one item to the other.Forecasts indicate that demand for soap and shampoo far exceeds production capacity.The profit per gallon of soap is $30 and per gallon of shampoo is $36.
A.Formulate a linear programming model that will maximize CCC's daily profit.
B.Suppose that the production of soap also yields a byproduct called Blyx.The manufacturing process yields 0.3 units of Blyx for every unit of soap.Up to 15 gallons of Blyx can be sold per day for canine shampoo at a profit of $10 per gallon.CCC must dispose of any excess of Blyx at a removal cost of $4 per gallon.Using X3 = the number of gallons of Blyx produced up to 15 gallons, and X4 = the number of gallons of Blyx produced over 15 gallons, modify the linear programming model for this problem.

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The Answer of The Carolina Chemical Company (CCC) makes two products, soap and shampoo, both in liquid form.The same two raw material inputs, glycerin and potash, and the same production line are used in the manufacture of each.Each production day, one ton of glycerin and two tons of potash are available.Each gallon of soap requires 8 pounds of glycerin and 32 pounds of potash, while a gallon of shampoo uses 12 pounds of glycerin and 19 pounds of potash.
CCC's production day is 8 full hours (480 minutes).Its production line can turn out 25 gallons of soap, or 20 gallons of shampoo, per hour.Only one product can be made at a time, but the line is easily changed over at negligible cost from one item to the other.Forecasts indicate that demand for soap and shampoo far exceeds production capacity.The profit per gallon of soap is $30 and per gallon of shampoo is $36.
A.Formulate a linear programming model that will maximize CCC's daily profit.
B.Suppose that the production of soap also yields a byproduct called Blyx.The manufacturing process yields 0.3 units of Blyx for every unit of soap.Up to 15 gallons of Blyx can be sold per day for canine shampoo at a profit of $10 per gallon.CCC must dispose of any excess of Blyx at a removal cost of $4 per gallon.Using X3 = the number of gallons of Blyx produced up to 15 gallons, and X4 = the number of gallons of Blyx produced over 15 gallons, modify the linear programming model for this problem.

The Carolina Chemical Company (CCC) Makes Two Products, Soap and Shampoo