Find the Matrix Product When Possible $30 \mathrm { gal }$

question 317

Multiple Choice

Find the matrix product when possible.
-Momma's ice cream shop sells three types of ice cream: soft-serve, chunky, and nonfat. Location I sells 14 gal of soft-serve, 80 gal of chunky, and $30 \mathrm { gal }$ of nonfat ice cream each day. Location II sells 28 gal of soft-serve and Location III sells 60 gal of soft-serve each day. Daily sales of chunky ice cream are 90 gal at Location II and 120 gal at Location III. At Location II, 38 gal of nonfat are sold each day, and $40 \mathrm { gal }$ of nonfat are sold each day at Location III.

Write a $3 \times 3$ matrix that shows the sales figures for the three locations, with the rows representing the three locations. The incomes per gallon for soft-serve, chunky, and nonfat ice cream are $\$ 7 , \$ 3$ , and $\$ 6$ , respectively. Write a $3 \times 1$ matrix displaying the incomes. Find a matrix product that gives the daily income at each of the three locations.

• A)
• \(\left[ \begin{array} { l } 714 \\ 870 \\ 648 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { l } 518 \\ 694 \\ 1020 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { l } 7 \\ 3 \\ 6 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { l } 548 \\ 664 \\ 1020 \end{array} \right]\)

---

Definitions:

Difference Between Values

The subtraction result of one value from another, often used to measure variation or change in data sets.

Dependent Populations

Populations in which members or samples do not independently exist from one another, often implying some relationship or mutual influence between the data sets.

Observations

Data collected during an experiment or study, often representing measured values of the variables of interest.

Matched Pairs Differences

The differences observed in the outcomes of treated vs. untreated units in a matched pairs experiment, vital for analyzing the effect of the treatment.