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Tyra will be setting up a stall during the school fair where she plans to sell cupcakes and donuts. She wanted to find out at what price she should sell each product to maximize her profit. She asked a market researcher to help her in this task. It was determined that at her current production capacity, each donut costs 22 pesos to make, while each cupcake costs 25 pesos to make. On the other hand, the market research study estimates that if a donut is to be sold at x pesos per piece, and a cupcake at y pesos per piece, then Tyra can expect to sell around (929 – 36x + 23y) donuts and around (1159 – 31y +17x) cinnamon rolls per week. 5. (a) How much should Tyra sell each piece of pastry if she wants to maximize her profit? What is maximum profit and how many of each pastry should she expect to sell during the school fair? Supply all solutions and computations. (b) Since the school was celebrating its 50th founding year, Tyra decided to fix the price of each cupcake to 50 pesos. At what price should she sell each donut so that she can still maximize her profit? What would be her maximum profit in this case?

Tyra will be setting up a stall during the school fair where she plans to sell cupcakes and donuts. She wanted to find out at what price she should sell each product to maximize her profit. She asked a market researcher to help her in this task. It was determined that at her current production capacity, each donut costs 22 pesos to make, while each cupcake costs 25 pesos to make. On the other hand, the market research study estimates that if a donut is to be sold at x pesos per piece, and a cupcake at y pesos per piece, then Tyra can expect to sell around (929 – 36x + 23y) donuts and around (1159 – 31y +17x) cinnamon rolls per week. 5. (a) How much should Tyra sell each piece of pastry if she wants to maximize her profit? What is maximum profit and how many of each pastry should she expect to sell during the school fair? Supply all solutions and computations. (b) Since the school was celebrating its 50th founding year, Tyra decided to fix the price of each cupcake to 50 pesos. At what price should she sell each donut so that she can still maximize her profit? What would be her maximum profit in this case?

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.CR: Review Problem Set
Problem 50CR
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Tyra will be setting up a stall during the school fair where she plans to sell cupcakes and donuts. She wanted to find out at what price she should sell each product to maximize her profit. She asked a market researcher to help her in this task. It was determined that at her current production capacity, each donut costs 22 pesos to make, while each cupcake costs 25 pesos to make. On the other hand, the market research study estimates that if a donut is to be sold at pesos per piece, and a cupcake at y pesos per piece, then Tyra can expect to sell around (929 – 36x + 23y) donuts and around (1159 – 31y + 17x) cinnamon rolls per week. 5. (a) How much should Tyra sell each piece of pastry if she wants to maximize her profit? What is maximum profit and how many of each pastry should she expect to sell during the school fair? Supply all solutions and computations. (b) Since the school was celebrating its 50th founding year, Tyra decided to fix the price of each cupcake to 50 pesos. At what price should she sell each donut so that she can still maximize her profit? What would be her maximum profit in this case?
Transcribed Image Text:Tyra will be setting up a stall during the school fair where she plans to sell cupcakes and donuts. She wanted to find out at what price she should sell each product to maximize her profit. She asked a market researcher to help her in this task. It was determined that at her current production capacity, each donut costs 22 pesos to make, while each cupcake costs 25 pesos to make. On the other hand, the market research study estimates that if a donut is to be sold at pesos per piece, and a cupcake at y pesos per piece, then Tyra can expect to sell around (929 – 36x + 23y) donuts and around (1159 – 31y + 17x) cinnamon rolls per week. 5. (a) How much should Tyra sell each piece of pastry if she wants to maximize her profit? What is maximum profit and how many of each pastry should she expect to sell during the school fair? Supply all solutions and computations. (b) Since the school was celebrating its 50th founding year, Tyra decided to fix the price of each cupcake to 50 pesos. At what price should she sell each donut so that she can still maximize her profit? What would be her maximum profit in this case?
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