Consider the Dorian Auto problem with the following LP formulation. 50 x1 +100x2 +2x2 +12x2 min...

 

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Consider the Dorian Auto problem with the following LP formulation. 50 x1 +100x2 +2x2 +12x2 min z = > 28 (HIW) > 24 (HIM) S.t. 7x1 2 X1 X1, X2 2 0 (x1: number of 1-min comedy ads, and x;: number of 1-min football ads) The optimal tableau is given below. RHS 320 X1 X2 e1 e2 a1 a2 7.5-M 1 -5 -7.5 5-M 1 -3/20 1/40 3/20 -1/40 7/80 3.6 1 1/40 -7/80 -1/40 1.4 Remember that for a minimization problem a tableau is optimal if and only if each variable has a non-positive coefficient in row 0 and the right-hand side of each constraint is non-negative. a) Find the range of values for the cost of a comedy ad (currently $50,000) for which the current basis remains optimal. b) Find the range of values for the number of required HIW exposures (currently 28 million) for which the current basis remains optimal. If 40 million HIW exposures were required, what would be the new optimal solution? c) Suppose an ad on news program costs $110,000, and reaches 12 million HIW and 7 million HIM. Should Dorian advertise on the news program? Consider the Dorian Auto problem with the following LP formulation. 50 x1 +100x2 +2x2 +12x2 min z = > 28 (HIW) > 24 (HIM) S.t. 7x1 2 X1 X1, X2 2 0 (x1: number of 1-min comedy ads, and x;: number of 1-min football ads) The optimal tableau is given below. RHS 320 X1 X2 e1 e2 a1 a2 7.5-M 1 -5 -7.5 5-M 1 -3/20 1/40 3/20 -1/40 7/80 3.6 1 1/40 -7/80 -1/40 1.4 Remember that for a minimization problem a tableau is optimal if and only if each variable has a non-positive coefficient in row 0 and the right-hand side of each constraint is non-negative. a) Find the range of values for the cost of a comedy ad (currently $50,000) for which the current basis remains optimal. b) Find the range of values for the number of required HIW exposures (currently 28 million) for which the current basis remains optimal. If 40 million HIW exposures were required, what would be the new optimal solution? c) Suppose an ad on news program costs $110,000, and reaches 12 million HIW and 7 million HIM. Should Dorian advertise on the news program?

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