Question

"The Acme Class Ring Company designs and sells two types of​ rings: the VIP and the SST. The company can produce up to 140 rings each​ day, using up to 350 total​ man-hours of labor. It takes 5 ​man-hours to make one VIP ring and 7 ​man-hours to make one SST ring. Let x represent the number of VIP​ rings, and let y represent the number of SST rings. Find the system of inequalities that describes this​ company's ring production"

Answer 1

• x + y ≤ 140
• 5x + 7y ≤ 350

Explanation:

You want the system of inequalities that describes the Acme Class Ring​ Company's ring production, given production limits of up to 140 rings per day and 350 total man-hours. Each of the x VIP rings takes 5 man-hours, and each of the y SST rings takes 7 man-hours.

Constraints

There are two constraints—one on the number of rings, and one on the number of man-hours. Each of these gives rise to an inequality describing the company's ring production.

x + y ≤ 140 . . . . . constraint on the number of rings

5x +7y ≤ 350 . . . . . constraint on the number of man-hours

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Additional comment

The constraint on man-hours means the constraint on production quantity will always be satisfied. The man-hour constraint means the company can produce at most 70 rings per day.