Hello I need help with problems 1,3,4

(3) City officials have realized the storefront space has more room than they estimated, and they can now fit all five businesses. They are keeping the target numbers of adults and children the same. (a) Write an augmented matrix representing this system. Don't solve it yet!Your team has been hired by your city to design a pair of storefronts for a business district. Your goal is to make the district more family friendly. Five businesses have applied for the storefronts, and each business would attract some number of adult and child customers to the district per day based on its storefront width. The two chosen businesses will need to attract a specic total number of adults and children to the district each day. Keeping in mind how wide each storefront would need to be to meet the target, your team is responsible for evaluating the suitability of business pairings. The business pairing will need to meet two conditions: (1) Attract two hundred (200) adults to the district every day. (2) Attract fty (50) children to the district every day. The table on the next page shows the ve candidate businesses and how many adult and child customers each one draws based on storefront width. Reminder: For a matrix in echelon form, a pivot position is the position of a leading 1. A free variable is a variable corresponding to a column with no pivot. Example: Pivot position m3 is a free variable Candidate Business list Candidate business Adult customers at- Children attracted per tracted per day day Hair salon 12 per meter of width 2 per meter of width Cafe 18 per meter of width 3 per meter of width Deli 12 per meter of width 3 per meter of width Shoe store 8 per meter of width 2 per meter of width Toy store 10 per meter of width 5 per meter of width .'he following plot shows the target number of adult and child customers represented as a tar. The vectors represent how many adult and child customers each candidate business rould attract if its storefront were 10 meters wide. 60 Toy store 50 - it Q: 40 1: g Deli Cafe 0.) H E g 20 She store air salon 10 50 100 150 200 250 300 Adults per day (1) Evaluate the following business pairings. For each, work as a group to answer the following question: Can the pairing reach the target? Consider implementing the following ideas: 0 Set up an augmented matrix representing the conditions the pairing needs to meet. 0 Determine how many pivots and how many free variables the system has. 0 Using the plot above, think about this system as adding two vectors (tiptotail) to try to arrive at the star. Adjusting the widths of the shops corresponds to adjusting the lengths of the vectors. 0 RREF is an option, although you might be able to get an answer without it! If the pairing works, explain why and draw your solution in the plot as two vectors added tiptotail. If not, explain why not. (a) A hair salon and a cafe (b) A hair salon and a toy store (0) A deli and a shoe store (d) A deli and a toy store (4) The city now wants your team to think about the entire multiblock business district. The city aims to achieve certain desired numbers of adult and child customers per day at each of 15 locations throughout the area. The city expects each of the 23 businesses in the district to attract a certain number of adult and child customers to each location per meter of width, similar to in part (1). (a) How many rows and columns does this system's matrix have? Draw an empty augmented matrix showing the matrix's shape