Optimizing Kiwifruit Packing: Shedz's Daily Tray Requirements and Cost Analysis

[Paulo2014]

I'm stuck...

Shedz processes two varieties of kiwifruit – green and gold. Constraints on daily packing are
as follows:
• At most, 2 000 trays can be packed in total.
• At most, 1 200 trays of green can be packed.
• A minimum of 200 trays of gold need to be packed.
• The ratio of the number of packed trays of green to gold must be no more than 5:2.
The ratio of the profit per tray of the green variety to the gold is 12:13.

Three types of tray are available; “all cardboard”, “cardboard / wood” and “all wood”, and Shedz
wishes to determine how many of each type to purchase.
The cost per tray is $1 for “all cardboard”, $2 for “cardboard / wood” and $4 for “all wood”. Shedz
budgets $5 000 per day for purchasing trays. Shedz requires 2 000 trays per day, with between 10%
and 30% of them being of the “all cardboard” type and as many as possible (subject to the above
criteria) being of the “cardboard / wood” type.
Using these criteria, determine Shedz’s daily requirement for each type of tray.

How do I do this?

 

[HallsofIvy]

First of all, you need to understand that this is NOT a probability problem! This is a "linear programming" problem. Also I think it would be a good idea to go back and read the proble again. You give a cost of each kind of tray but I can see nowhere in the problem where that information is used or needed.