Robot Primates, Inc. is the world\'s leading manufacturer of robotic monkeys and

Question

Robot Primates, Inc. is the world's leading manufacturer of robotic monkeys and gorillas.
To meet demand, Robot Primates must produce at least 100 robotic monkeys and 80 robotic gorillas a
day. Due to limitations in productions capacity, they can produce no more than 200 robotic monkeys
and 170 robotic gorillas, and due to a shipment contract, they must produce at least 200 robotic
primates per day.
Robotic Primates found that they net a $2,000 loss for each robotic monkey they produce, but make
a $5,000 pro t for each robotic gorilla produced. How many of each type of robo-primate should they
produce to maximize pro ts?

Explanation / Answer

This is an easy optimization problem.

Assume they produce x robotic monkeys and y robotic gorillas.

Since "to meet demand, Robot primates must produce at least 100 robotic monkeys and 80 robotic gorillas a day", x > = 100

and y > = 80.

Since "due to limitations in productions capacity, they can produce no more than 200 robotic monkeys and 170 robotic gorillas", x < = 200 and y < = 170.

Since " due to a shipment contract, they must produce at least 200 robotic primates per day", x+y > = 200

Since "Robotic Primates found that they net a $2,000 loss for each robotic monkey they produce, but make a $5,000 for each robotic gorilla produced" , money = 5,000*y - 2,000*x.

It;s easy to see that, when x=200, y=170, moeny reaches maximum.

money maximum = 5000*170 - 2000*200=450000

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