The Research and Development Division of the Emax Corporation has developed three new products. A decision now needs to be made on which mix of these products should be produced. Management wants primary consideration given to three factors: total profit, stability in the workforce, and achieving an increase in the companys earnings next year from the $75 million achieved this year. In particular, using the units given in the table below, they want to

Market share for Product 1 = 0.5x1 + 0.2x3,

Market share for Product 2 = 0.3x2 + 0.2x3.

A total of $55 million is available for the three advertising campaigns, but management wants at least $10 million devoted to the third campaign. If both market share goals cannot be achieved, management considers each 1 percent decrease in the market share from the goal to be equally serious for the two products. In this light, management wants to know how to most effectively allocate the available money to the three campaigns.

(a) Formulate a goal programming model for this problem.

(b) Reformulate this model as a linear programming model.

(c) Use the simplex method to solve this model.