# Optimization Help

• Sep 23rd 2009, 02:59 PM
Kapow
Optimization Help
Hello Everyone, I have a little problem here. I have a question and I am completely lost. It seems as if I understand in class and when I arrive to do my homework I forget everything that was taught to me.

Here is the Optimization Problem:

Every year, the Boy Scouts association sells calendars to raise money. Two types of calendars are sold:
-Wall Calendars at 4:00\$ each
-Desk Calendars at 2.00\$ each.
The profit on the sale of a wall calendar is 2\$. On the desk calendar, the profit is only 0.50\$ each.
To cover their expenses, the scouts must sell at least twice as many wall calendars as desk calendars. F
From previous years, they know they will sell between 300 and 600 calendars.
How many calendars of each type must the scouts sell to maximize their profit?

Let: X: Number of wall calendars
Y: Number of desk calendars.
What are the constraints?
How many Wall calendars and Desk calendars must the scouts sell?

Thank you so much for all help. Sorry my first post involves me asking a question. I will probably stick around this forum ;)

• Sep 23rd 2009, 11:51 PM
CaptainBlack
Quote:

Originally Posted by Kapow
Hello Everyone, I have a little problem here. I have a question and I am completely lost. It seems as if I understand in class and when I arrive to do my homework I forget everything that was taught to me.

Here is the Optimization Problem:

Every year, the Boy Scouts association sells calendars to raise money. Two types of calendars are sold:
-Wall Calendars at 4:00\$ each
-Desk Calendars at 2.00\$ each.
The profit on the sale of a wall calendar is 2\$. On the desk calendar, the profit is only 0.50\$ each.
To cover their expenses, the scouts must sell at least twice as many wall calendars as desk calendars. F
From previous years, they know they will sell between 300 and 600 calendars.
How many calendars of each type must the scouts sell to maximize their profit?

Let: X: Number of wall calendars
Y: Number of desk calendars.
What are the constraints?
How many Wall calendars and Desk calendars must the scouts sell?

Thank you so much for all help. Sorry my first post involves me asking a question. I will probably stick around this forum ;)

You want to maximise profit, so the objective is:

2X+0.5Y

Now you have to reformulate "To cover their expenses, the scouts must sell at least twice as many wall calendars as desk calendars" as a constraint in terms of X and Y.

Similarly formulate constraints from "From previous years, they know they will sell between 300 and 600 calendars"

Remember you also have non-negativity constraints on X and Y.

Solve this using the graphical method that you have been shown in class and/or your text.

CB