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)
• \(\left[ \begin{array} { l } 548 \\ 664 \\ 1020 \end{array} \right]\)

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Definitions:

Stepwise Regression

Stepwise regression is a statistical method of building predictive models by sequentially adding or removing variables based solely on their statistical significance.

Multiple Regression

A procedure within statistics for modeling how various independent variables impact a single dependent variable.

Independent Variables

Variables in an experiment or model that are manipulated or selected by the researcher to determine their effect on the dependent variable.

Iterative Procedure

An iterative procedure is a process that repeats steps to achieve a desired goal or solution, often used in mathematical algorithms and problem-solving.