Question

You produce two products. You have to produce at least 30 of product 1 at $3 per unit and at least 20 of product 2 at $5 per unit and your total production cost cannot exceed $340. If product #1 earns a profit of $10 per unit and product #2 earns a profit of $15 per unit, what is the combination of product 1 and 2 that will maximize profit?

Answer 1

Let the required quantity of product 1 be p and the required quantity of product 2 be q.
The maximum profit will occur at the maximum allowable total production cost of $340. Therefore
3p + 5q = 340 ..............(1)
Also the maximum profit will occur when the minimum allowable quantity of product 1 is produced, the reason being that each product 2 earns 50% more profit than each product 2. Plugging the minimum allowable quantity of product 1 (30 units) into equation (1) gives
(3 * 30) + 5q = 340
90 + 5q = 340 ...........(2)
Now you just need to solve equation (2) to find q, the required quantity of product 2.
Can you do that?