Question

A political party is planning a half hour television show. The show will have at least 33 minutes of direct requests for money from viewers. Three of the​ party's politicians will be on the show - a ​senator, a​ congresswoman, and a governor. The​ senator, a party​ "elder statesman," demands that he be on screen for at least twice as long as the governor. The total time taken by the senator and the governor must be at least twice the time taken by the congresswoman. Based on a​ pre-show survey, it is believed that 31, 26 and 41 ​(in thousands) viewers will watch the program for each minute the​ senator, congresswoman, and​ governor, respectively, are on the air. Find the time that should be allotted to each politician in order to get the maximum number of viewers. Find the maximum number of viewers.

The quantity to be​ maximized, z, is the number of viewers in thousands. Let x1 be the total number of minutes allotted to the​ senator, x2 be the total number of minutes allotted to the​ congresswoman, and x3 be the total number of minutes allotted to the governor. What is the objective​ function?

Answer 1

Let x1 be the total number of minutes allotted to the​ senator

Let x2 be the total number of minutes allotted to the​ congresswoman

Let x3 be the total number of minutes allotted to the governor.

Constraints:

Solving the equations, we get

x1 = 22, x2 = 0, x3 = 11

Maximum viewership = 31(22) + 41(11) = 1133 thousand viewers

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