8 Consider the Dorian Auto problem (Example 2 of Chapter 3):

(x1 = number of comedy ads, and x2 = number of football ads). The optimal tableau is given in Table 13. Remember that for a min problem, a tableau is optimal if and only if each variable has a nonpositive coefficient in row 0 and the right-hand side of each constraint is nonnegative.
a Find the range of values of the cost of a comedy ad (currently $50,000) for which the current basis remains optimal.
b Find the range of values of 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 a news program costs $110,000 and reaches 12 million HIW and 7 million HIM. Should Dorian advertise on the news program?
9 Show that if the right-hand side of the ith constraint is increased by , then the right-hand side of the optimal tableau is given by (original right-hand side of the optimal tableau) +
(column i of B^-1).

Transcribed Image Text:

min z = 50x + 100x2 s.t. 7x + 2x2 = 28 (HIW) 2x + 12x224 (HIM) x1,x20