introduction: cake baking Kate has a business baking and selling chocolate cakes and carrot cakes. She would like to investigate the number of each cake she should make in order to make the best use of her time and maximise the profit from her small business. In this assessment task you need to find the number of each type of cake that Kate should bake in order to maximise her profit. Show all the graphs and equations that you have used and any relevant calculations. Clearly communicate your method using appropriate mathematical statements. task 1. Use the information in Resource 1 (Kates cake business constraints and income predictions) to write a report which identifies: • the maximum profit that Kate can make. • the number of chocolate cakes and carrot cakes that Kate needs to sell to maximise the profit.
2. As Kate gets more efficient at making cakes she is able to reduce the time it takes her to prepare a chocolate cake down to 24 minutes, and the time to prepare a carrot cake down to 32 minutes. She also decides to reduce the overall preparation time that she spends down to 1320 minutes [22 hours]. How will these reduced times affect the number of each cake that she bakes and the overall profit? • Use the adjusted times to identify the maximum profit that Kate can make. • Identify the number of chocolate cakes and carrot cakes that Kate now needs to sell to maximise the profit.
2. As Kate gets more efficient at making cakes she is able to reduce the time it takes her to prepare a chocolate cake down to 24 minutes, and the time to prepare a carrot cake down to 32 minutes. She also decides to reduce the overall preparation time that she spends down to 1320 minutes [22 hours]. How will these reduced times affect the number of each cake that she bakes and the overall profit? • Use the adjusted times to identify the maximum profit that Kate can make. • Identify the number of chocolate cakes and carrot cakes that Kate now needs to sell to maximise the profit.