Question

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 belleved that 38 , 44 , and 50 (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 vlewers 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?z=x₁+x₂+x₃

Answer 1

The objective function in this problem is to maximize the number of viewers. To solve this optimization problem, you can use linear programming techniques to find the optimal values of x1, x2, and x3 that maximize the objective function z.

Step-by-step explanation:

The objective function in this problem is to maximize the number of viewers. The number of viewers in thousands can be represented by the equation z = x1 + x2 + x3, where x1, x2, and x3 represent the total number of minutes allotted to the senator, congresswoman, and governor, respectively. To find the maximum number of viewers, we need to solve the problem under the given constraints:

1. There must be at least 9 minutes of direct requests for money from viewers.
2. The senator's screen time must be at least twice as long as the governor's.
3. The total time taken by the senator and governor must be at least twice the time taken by the congresswoman.

To solve this optimization problem, you can use linear programming techniques such as the simplex method or graphical method to find the optimal values of x1, x2, and x3 that maximize the objective function z, subject to the given constraints.