Optimization: Unknown function: "200 000 catalogs need to be printed...."

[GeekOfMath]

Hello everyone!
I need help with finding the functions within the information of this problem:

200 000 catalogs need to be printed. The two costs for the print run are hours the presses will be required to work and the plates needed to print.
The presses cost $8/hr to run and will produce 1200 impressions per hour.
Each impression produces x catalogs where x is the number of plates used on the printing presses. Each plate cost $2 to prepare.

Question: How many plates should be made to ensure it is economical?

In advance thanks for all your help!:wink:

 

[tkhunny]

I'm thinking you should create an equation that represents your cost function. Let's see your efforts.

 

[GeekOfMath]

I'm thinking you should create an equation that represents your cost function. Let's see your efforts.

I'm thinking something like this: C = 8t +2x
Where t = time in hours and x = number of plates

 

[HallsofIvy]

Go a little further with that. "Each impression produces x catalogs" so if there are x plates then 1200 impressions per hour will produce 1200x catalogs per hour. In t hours, with x plates, you can produce 1200xt catalogs. The cost will be, as you say, C= 8t+ 2x and you want to produce 200000 catalogs so you must have 1200xt= 200000. You want to minimize C= 8t+ 2x with the condition 1200xt= 200000.