Bakery R Us uses a set model to determine the total cost of a package of chocolate mini cakes purchased through Amazon Prime’s membership. The base handling fee, on any package, is $4.00. The cost for the first 20 chocolate mini cakes is $8.00 per mini cakes. If you order more than 20 chocolate mini cakes, Bakery R Us gives you a deal and only charges $5.50 for each additional chocolate mini cake that you order over 20. Bakery R Us limits the number of chocolate mini cakes that can be ordered to

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Bakery R Us uses a set model to determine the total cost of a package of chocolate mini cakes purchased through Amazon Prime’s membership. The base handling fee, on any package, is $4.00. The cost for the first 20 chocolate mini cakes is $8.00 per mini cakes. If you order more than 20 chocolate mini cakes, Bakery R Us gives you a deal and only charges $5.50 for each additional chocolate mini cake that you order over 20. Bakery R Us limits the number of chocolate mini cakes that can be ordered to 50 chocolate mini cakes per order

Piece-wise functions are used to represent functions that have inputs in different range.The piece-wise function is: [tex]y =\left[\begin{array}{ccc} 4+ 8x,&0 \le x \le 20\\54+ 5.5x,&21 \le x \le 50\end{array}\right[/tex]Let the number of packages be x, and the total cost of the package be yWe have:[tex]Base = 4.00[/tex][tex]R_1 = 8.00[/tex] ---rate per package for the first 20[tex]R_2 = 5.50[/tex] ---rate per package in excess of 20For the first 20, we have:[tex]y = Base + R_1 \times x[/tex][tex]y = 4+ 8\times x[/tex][tex]y = 4+ 8x[/tex]Where[tex]0 \le x \le 20[/tex] i.e. from 0 to 20 packagesFor packages above 20 but less than 50 (the maximum)[tex]y = Base + R_1 \times 20 + R_2 \times (x - 20)[/tex][tex]y = 4 + 8 \times 20 + 5.5 \times (x - 20)[/tex][tex]y = 4 + 160 + 5.5x - 110[/tex]Collect like terms[tex]y = 4 + 160 - 110+ 5.5x[/tex][tex]y = 54+ 5.5x[/tex]Where[tex]21 \le x \le 50[/tex] i.e. from 21 to 50 packagesSo, the piece-wise function is:[tex]y =\left[\begin{array}{ccc} 4+ 8x,&0 \le x \le 20\\54+ 5.5x,&21 \le x \le 50\end{array}\right[/tex]Read more about piece-wise functions at:https://brainly.com/question/6111304

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