# A political party is planning a ninety-minute television

Last updated: 7/24/2022

A political party is planning a ninety-minute television show. The show will have at least 9 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 39, 44, and 49 (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? The senator should be allotted minutes. (Simplify your answer.) The congresswoman should be allotted minutes. (Simplify your answer.) The governor should be allotted minutes. (Simplify your answer.) The maximum number of viewers is (Simplify your answer.)

Show Answer