A farmer's three children, Amy, Beth and Chad, run three roadside produce stands during the summer months. One weekend they all sell watermelons, yellow squash and tomatoes. The matrices A and B tabulate the number of pounds of each product sold by each sibling on Saturday and Sunday
The matrix C gives the price per pound (in dollars) for each type of produce that they sell.
Perform each of the following matrix operations, and interpret the entries in each result.
a.) AC b.) BC c.) A+B d.) (A+B)C
a.) AC=[Matrix A][Matrix B]=[120(0.10)+50(0.50)+60(1.00)40(0.10)+25(0.50)+30(1.00)60(0.10)+30(0.50)+20(1.00)]=[9746.541]
When we take the inner product of row in A with a column in B, we are multiplying the total number of weight to its corresponding unit price per weight. Thus, AC shows the profit of the siblings on Saturday.
The values 97,46.5 and 41 are the profit of Amy, Beth and Chad respectively.
b.) BC=[Matrix B][Matrix C]=[100(0.10)+60(0.50)+30(1.00)35(0.10)+20(0.50)+20(1.00)60(0.10)+25(0.50)+30(1.00)]=[7033.548.5]
Same as from part (b). But its the sibling's profit on Sunday.
c.) A+B=[Matrix A]+[Matrix B]=[120+10050+6060+3040+3525+2030+2060+6030+2520+30]=[220110907545501205550]
This shows the total number of weight sold by each child on Saturday and Sunday.
d.) (A+B)C=[220110907545501205550][0.100.501.00]=[220(0.10)+110(0.50)+90(1.00)75(0.10)+45(0.50)+50(1.00)120(0.10)+55(0.50)+50(1.00)]=[1678089.5]
This shows the total profit from each child on Saturday and Sunday. The values 167,80 and 89.5 are the profit of Amy, Beth and Chad respectively.
Friday, June 15, 2018
College Algebra, Chapter 7, 7.2, Section 7.2, Problem 48
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