How would you go about writing and solving the inequality to know how many items you can manufacture while staying within your $2000 budget?

Question

you are creating a business to earn some extra income over the summer. you decide to sell one product that costs you $2.50 to make. you have a total of $2000 to put towards the cost of starting your business. How would you go about writing and solving the inequality to know how many items you can manufacture while staying within your $2000 budget?

Answer 1

If Q is the quantity of items you can make without exceeding $2000, then the inequality is 2.5Q≤2000, Q≤2000/2.5, Q≤800.

So to stay within budget you can make no more than 800 items, but, of course, when you’ve eventually sold the items at $P each you will have made $800P.

(The profit on each item is P-2.5 dollars. If you sell q items, your sales would bring in qP dollars and it would cost you 2.5q dollars to make q items. Revenue-costs is qP-2.5q=q(P-2.5) dollars profit.)