A small grocer finds that the monthly sales y (in $) can be approximated as a function of the amount spent advertising on the radio x_1 (in $) and the

Wierzycaz 2020-11-06 Answered
A small grocer finds that the monthly sales y (in $) can be approximated as a function of the amount spent advertising on the radio x1
(in $) and the amount spent advertising in the newspaper x2 (in $) according to y=ax1+bx2+c
The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months.
 Advertising, x1 Advertising, x2sales, y$2400$800$36,000$2000$500$30,000$3000$1000$44,000
a) Use the data to write a system of linear equations to solve for a, b, and c.
b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.
c) Write the model y=ax1+bx2+c
d) Predict the monthly sales if the grocer spends $250 advertising on the radio and $500 advertising in the newspaper for a given month.
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Expert Answer

svartmaleJ
Answered 2020-11-07 Author has 92 answers
y=ax1+bx2+c
We have to determine the function:
{2400a+800b+c=360002000a+500b+c=300003000a+1000b+c=44000
Set up a system of equations for a,b,c:
[24008001|3600020005001|30000300010001|44000]
b) Build the augmented matrix:
[100|12010|4001|4000]
Use a graphing utility to find the reduced row-echelon form of the augmented matrix: a=12,b=4,c=4000
c) Determine a,b,c:
y=12x1+4x2+4000
write the model y that fits the data:
y=12(2500)+4(500)+4000=36000
d) Determine y for x1=2500,x2=500
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