How to formulate constraints given the following information

Question

The following question was given in one of my class but none of us got the use of the market requirements in the problem:

A form produces and sells three products namely Product1, Product2 and Product3 . The respective unit profit earned are 4.00dollars for Product1 , 3.00dollars for Product2 and 5.00dollars for Product3. Each product is processed on two machines, Machine1 and Machine2 . A unit of Product1 requires 4minutes of processing time on Machine1 and 2minutes of processing time on Machine2. A unit of Product2 requires 3minutes of processing time on Machine1 and 2minutes of processing time on Machine2. A unit of Product3 requires 5minutes of processing time on Machine1 and 4minutes of processing time on Machine2. The available capacity on Machine1 is 2000 machine minutes and that on Machine2 is 2500 machine minutes.
For market requirement, the firm must produce at least 100 units of Product1 but not more than 150 units of the product, at least 200 units of Product2, and at least 50 units of Product3.

How do you formulate constraints from this information?

Answer 1

Let

$x_1$: Amount of product 1

$x_2$: Amount of product 2

$x_3$: Amount of product 3

In my opinion defining the variables is the most important step.

The objective function expresses the total profit:

$\texttt{max} \ \ 4x_1+3x_2+5x_3 $

Constraint for capacity of machine 1:

Product 1 requires 4 minutes on machine 1, product 2 requires 3 minutes of processing time on machine 1 and a unit of product 3 requires 5 minutes.

The available capacity on machine 1 is 2000 machine minutes.

The total required machine minutes have to be smaller or equal to 2,000.

$4x_1+3x_2+5x_3 \leq 2,000$

Can you formulate the constraint for the second machine ?