The Growall Fertilizer Company produces three types of fertilizer—Supergro, Dynaplant, and Soilsaver. The company has the capacity to produce a maximum of 2,000 tons of fertilizer in a week. It costs $800 to produce a ton of Supergro, $1,500 for Dynaplant, and $500 for Soilsaver.
The production process requires 10 hours of labor for a ton of Supergro, 12 hours for a ton of Dynaplant, and 18 hours for a ton of Soilsaver. The company has 800 hours of normal production labor available each week. Each week the company can expect a demand for 800 tons of Supergro, 900 tons of Dynaplant, and 1,100 tons of Soilsaver. The company has established the following goals, in order of their priority:
(1) The company does not want to spend over $20,000 per week on production, if possible.
(2) The company would like to limit overtime to 100 hours per week.
(3) The company wants to meet demand for all three fertilizers; however, it is twice as important to meet the demand for Supergro as it is to meet the demand for Dynaplant, and it is twice as important to meet the demand for Dynaplant as it is to meet the demand for Soilsaver.
(4) It is desirable to avoid producing under capacity, if possible.
(5) Because of union agreements, the company wants to avoid underutilization of labor.
a. Formulate a goal programming model to determine the number of tons of each brand of fertilizer to produce to satisfy the goals.
b. Solve this model by using the computer.