Question

yummy yogurt sells three types of yogurt: nonfat, regular, and super creamy, at three locations. location i sells 50 gal of nonfat, 60 gal of regular, and 10 gal of super creamy each day. location ii sells 20 gal of nonfat, and location iii sells 70 gal of nonfat each day. daily sales of regular yogurt are 50 gal at location ii and 110 gal at location iii. at location ii, 50 gal of super creamy are sold each day, and 20 gal of super creamy are sold each day at location iii.
a) write a 3×3 matrix that shows the sales figures for the three locations, with the rows representing the three locations.
nonfat regular creamy
location i
location ii
location iii
\

$$\begin{bmatrix} \\square & \\square & \\square \\\\ \\square & \\square & \\square \\\\ \\square & \\square & \\square \\end{bmatrix}$$

Explanation:

Step1: Identify rows and columns

Rows: Location I, II, III. Columns: Nonfat, Regular, Creamy (Super Creamy).

Step2: Extract data for Location I

Nonfat: 50, Regular: 60, Creamy: 10. So row 1: [50, 60, 10].

Step3: Extract data for Location II

Nonfat: 20, Regular: 50 (daily regular at II), Creamy: 50 (daily super creamy at II). So row 2: [20, 50, 50].

Step4: Extract data for Location III

Nonfat: 70, Regular: 110 (daily regular at III), Creamy: 20 (daily super creamy at III). So row 3: [70, 110, 20].

Step5: Form the matrix

Combine rows into a 3×3 matrix:

$$\begin{bmatrix} 50 & 60 & 10 \\ 20 & 50 & 50 \\ 70 & 110 & 20 \end{bmatrix}$$

Answer:

$$\begin{bmatrix} 50 & 60 & 10 \\ 20 & 50 & 50 \\ 70 & 110 & 20 \end{bmatrix}$$