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Sagot :
The system of inequalities be
3x+2y ≤ 25, 4x+6y ≤ 37
1) Maximum number of sundaes possible exists 9.
2) Maximum number of milkshakes possible exists 6.
3) Combination that uses the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.
What is system of inequalities?
A system of inequalities exists the system where the set of more than one inequalities in more than or equivalent to one variable.
Given: A sundae needs 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries.
Ramses have to create sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries.
Let x represent the number of sundaes he creates and y the number of milkshakes he creates.
We represent in tabular form,
Sundae(x) Milkshake(y) Total
Ice-cream 3 2 3x+2y
Strawberries 4 6 4x+6y
System of inequalities:
Sundaes and milkshakes with at most 25 ice-cream scoops exist
33x+2y ≤ 25.
Sundaes and milkshakes with at most 37 strawberries exist 4x+6y ≤ 37.
1) Maximum number of sundaes possible:
Maximum number of sundaes possible when y = 0
From the graph y = 0 at x = 9.25
Therefore, the maximum number of sundaes possible exists at 9.
2) Maximum number of milkshakes possible:
Maximum number of milkshakes possible when x = 0
From the graph x = 0 at y = 6.167
Therefore, the maximum number of milkshakes possible exists at 6.
3) Combination that utilizes the most of both Ice-cream and Strawberries:
A combination of both is possible there exists an intersection of both the equation.
From the graph, the intersection point exists x = 7.6 and y = 1.1.
Therefore, the Combination that utilizes the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.
To learn more about system of inequalities refer to:
https://brainly.com/question/9290436
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