Two coffee house chains, Startrak and Mill Mountain, dominate the Columbus market. Startrak has developed three new marketing strategies, 1, 2, and 3, for the fall season, which include various combinations of media and print advertising, and promotions Mill Mountain knows Startrak plans a marketing campaign, and it has developed three strategies of its own, A, B and C, to offset those of Startrak. The following table shows the percentage market share gains (or losses) expected by Startrak for each of its three strategies given the possible strategies of Mill Mountain. Startrak obviously wants to maximize its gains, whereas Mill Mountain wants to minimize Startrak’s gains.

Startrak wants to select a mix of its strategies such that its gains are the same regardless of the strategies of Mill Mountain; Startrak’s objective is to select a “mixed strategy” (i.e., the probabilities of selecting each of its three strategies) in such a way as to maximize its minimum expected gains. This is a problem in the field known as “Game Theory,” and this decision scenario can be formulated and solved as a linear programming problem. If the value of the game that Startrak wants to maximize is denoted by “V,” and the probabilities that Startrak will select strategies 1, 2 and 3, are respectively ;P₁,< ;P₂,< and ;P₃,< formulate and solve a linear programming model for this game situation.

Transcribed Image Text:

Startrak Strategies 1 2 لما 3 Mill Mountain Strategies A 8 -2 1 B -3.5 7 6 C 5.5 4 نما