Question 1170735: A small software company publishes computer games, educational software, and utility software. Their business strategy is to market a total of 24 new programs each year, at least two 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?
Thank you!
Answer by ikleyn(52772)   (Show Source):
You can put this solution on YOUR website! .
A small software company publishes computer games, educational software, and utility software.
Their business strategy is to market a total of 24 new programs each year, at least two 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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This problem is more to exercise your common sense, rather than make complicated calculations.
Let G = # of games;
E = # of educational
U = # of utilities.
Then the constraints are
G + E + U = 24
G >= 2
U <= 2E
P = 5000G + 8000E + 6000U (the Profit function).
Now the common sense dictates this strategy:
Sell the most profitable product (E, educational) as much as possible;
sell the worst profitable product (G, games) as few as possible (=2).
do not sell the intermediate profitable product U, at all.
So, the optomal solution is G = 2, E = 22, U = 0. ANSWER
Solved.
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