Word problem?

Question

How do I go about formulating this with a list of variables and constraints?

Three new products are to be produced.
Total production should range between 1,000 and 2,000 units
At least 1 item of product 2 is made for every item of product 1
The total production of product 1 and product 2 should be half the production of product 3
The first 12 units of product 1 earn $17/unit, additional units earn $15/unit.
Product 2 earns $10/unit
The frist 5 units of product 3 earn $20/unit, the next 15 units earn $18/unit, the next 2,000 units earn $9/unit

Answer 1

OK. Give the number of products produced a variable. e.g. Number of product 1 produced = a. Product 2 = b. Product 3 = c.

Now work down your list of constraints.

1000 <= a + b + c <= 2000

b >= a

c = 2(a + b)

Get the idea?

The next lot indicate the earnings of the various products. Presumably you are after the total earnings, so -

12 * 17 + (a - 12) * 15 plus
10b plus
5 * 20 + 15 * 18 + (c-20) * 9

You also need to check that the numbers of each product are sufficient for the above equation to hold, i.e. a > 12 and 20 < b < 2020