Tiffany sells two kinds of homemade tomato sauce. A quart of her Tuscan sauce requires 6 tomatoes and 1 cup of oil. A quart of her marinara sauce requires 5 tomatoes and 1 1/4 cups of oil. She makes $4 profit on each quart of her Tuscan sauce and $5 profit on each quart of her marinara sauce. She has 45 tomatoes and 10 cups of oil on hand. Tiffany wants to maximize their profits from selling the sauce.

Let x represent the number of quarts of Tuscan sauce and y represent the number of quarts of marinara sauce Tiffany makes.

What are the constraints for the problem?

Question

Mathematics

Brent Parsons

25 February, 22:55

Tiffany sells two kinds of homemade tomato sauce. A quart of her Tuscan sauce requires 6 tomatoes and 1 cup of oil. A quart of her marinara sauce requires 5 tomatoes and 1 1/4 cups of oil. She makes $4 profit on each quart of her Tuscan sauce and $5 profit on each quart of her marinara sauce. She has 45 tomatoes and 10 cups of oil on hand. Tiffany wants to maximize their profits from selling the sauce.

Let x represent the number of quarts of Tuscan sauce and y represent the number of quarts of marinara sauce Tiffany makes.

What are the constraints for the problem?

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Answers (1)

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Brendon Mathis · Answer 1

X = # of quarts of Tuscan sauce = > 6x tomatoes + 1x cups of oil

y = # of quarts of marinara sauce=> 5y tomatoes + 1.25y cups of oil

Function to maximize: profit = 4x + 5y

Restrictions:

# of tomatoes: 6x + 5y ≤ 45

# of cups of oil: x + 1.25 y ≤ 10

# of quarts of Tuscana sauce: x ≥ 0

# of quarts of marinara sauce y ≥ 0