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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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.

svartmaleJ · Accepted Answer

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

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

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