Linear Programming - Math

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, 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 the company publish annually for maximum profit?

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  1. let x,y,z be the number of games, education, utility programs sold.

    you want to
    maximize 5000x+8000y+6000z subject to
    x+y+z = 36
    x >= 4
    z <= 2y

    Looks like (x,y,z) = (4,32,0)

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  2. im not really understand this topic

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