Question

factory manufactures two types of gadgets, regular and premium. Each gadget requires the use of two operations, assembly and finishing, and there are at most $120$ hours available for each operation. A regular gadget requires $1$ hour of assembly and $2$ hours of finishing, while a premium gadget needs $3$ hours of assembly and $1$ hour of finishing. Due to other restrictions, the company can make at most $70$ gadgets a week.

Let $x$ be the number of regular gadgets, and let $y$ be the number of premium gadgets. Enter the inequality for each restriction. Each inequality should be of the form $ax + by \le c,$ where $a,$ $b,$ $c$ are positive integers with no common factor other than $1.$

Answer 1

Assembly time: x + 3y ≤ 120

Finishing time: 2x + y ≤ 120

Maximum gadgets: x + y ≤ 70

(Also x ≥ 0, y ≥ 0.)