Question

An ice-cream shop makes x gallons of ice cream and y gallons of frozen yogurt each day. The shop developed the following constraints to manage production and minimize cost:

x>0

y>0

3x+7y<200

y≥2x−20

Which point (x,y) represents a viable combination of ice cream and frozen yogurt the shop can make in a day and satisfy the constraints?

Answer 1

The ice-cream shop needs to find a viable combination of ice cream and frozen yogurt that satisfies the given constraints.

Step-by-step explanation:

The ice-cream shop has the following constraints:

• x > 0
• y > 0
• 3x + 7y < 200
• y ≥ 2x − 20

We need to find the point (x, y) that satisfies these constraints. To do that, we can graph the inequalities on a coordinate plane and find the region that satisfies all the constraints. The viable combination of ice cream and frozen yogurt the shop can make in a day and satisfy the constraints is the region that is shaded.