Thread: Optimization problem #3

A printing company has eight presses, each of which can print 3600 copies per hour. It costs $5.00 to set up each press for a run and 10+6n dollars to run n presses for 1 h. How many presses should be used to print 50,000 copies of a poster most profitably.

Profit is revenue minus cost. In this case, revenue is presumed to be a fixed value because the number of copies is fixed at 50,000. Therefore, maximizing profit in this problem is the same as minimizing cost.

Can you come up with a solution that minimizes the total cost?

Originally Posted by drumist

Can you come up with a solution that minimizes the total cost?

I wasn't able to come up with a formula for the total cost.

Originally Posted by alexmahone

A printing company has eight presses, each of which can print 3600 copies per hour. It costs $5.00 to set up each press for a run and 10+6n dollars to run n presses for 1 h. How many presses should be used to print 50,000 copies of a poster most profitably.

Let be the number of presses used.
Firstly, we have to assume that
(i)the work will be finished in one run;
(ii)all presses begin to run at the same time;
Then, we can have the following formula that denotes the cost: