Question

A small software company publishes computer games and educational and utility software. Their business strategy is to market a total of 36 new programs each year, with at least four of these being games. The number of utility programs published is never more than twice the number of educational programs. On average, the company makes an annual profit of $ 5000 on each computer game, $ 8000 on each educational program, and $ 6000 on each utility program. How many of each type of software should they publish annually for maximum profit?

Answer 1

To determine the optimal number of each type of software the company should publish annually for maximum profit, set up a linear programming problem.

Step-by-step explanation:

To determine the optimal number of each type of software the company should publish annually for maximum profit, we can set up a linear programming problem. Let's denote the number of games as G, educational programs as E, and utility programs as U.

The objective function is to maximize profit, which can be expressed as:

Profit = 5000G + 8000E + 6000U

Subject to the following constraints:

1. Number of programs: G + E + U = 36
2. At least four games: G ≥ 4
3. Utility programs ≤ 2 * educational programs: U ≤ 2E

We can solve this linear programming problem using graphical or algebraic methods to find the optimal values for G, E, and U.