Chemco Corporation produces a chemical mixture for a specific customer in 1,000-pound batches. The mixture contains three ingredients—zinc, mercury, and potassium. The mixture must conform to formula specifications that are supplied by the customer. The company wants to know the amount of each ingredient it needs to put in the mixture that will meet all the requirements of the mix and minimize total cost.
The customer has supplied the following formula specifications for each batch of mixture:
The mixture must contain at least 200 pounds of mercury.
The mixture must contain at least 300 pounds of zinc.
The mixture must contain at least 100 pounds of potassium.
The ratio of potassium to the other two ingredients cannot exceed 1 to 4.
The cost per pound of mercury is $400; the cost per pound of zinc, $180; and the cost per pound of potassium, $90.
a. Formulate a linear programming model for this problem.
b. Solve the model formulated in (a) by using the computer.