In this questions we will set up a system of equations It ma

In this questions we will set up a system of equations. It may be helpful to review the basics of linear systems here.

Suppose you\'re the owner of a smoothy shop and that you have three resources available to make smoothies: bananas, blueberries, and strawberries. You sell three types of smoothies, and each type requires a different amount of each resource. The Classic includes 2 bananas, 2 cups of blueberries, and 1 cup of strawberries. The Blue uses 4 cups of blueberries and 2 cups of strawberries. The Strawnana has just 2 bananas and 2 cups of strawberries. At the end of the day you have used 52 Bananas, 56 cups of blueberries, and 40 cups of strawberries.

For this problem, construct the matrix problem

Ax=bAxb

How many Strawnanas did you sell during the day?

Solution

Let x, y and z be classic , blue and strawnana\'s sold respectively

52 = 2x + 2z

56 = 2x + 4y

40 = x + 2y + 2z

A = [(2,02,2), (2,4,0), (1,2,2)] X = [x,y,z]^T B = [52, 56, 40]^T

Solving the above system gives x = 20, y = 4 and z = 6.

Number of strawnanas sold = 6.