cheersquad2345
New member
- Joined
- Aug 23, 2022
- Messages
- 1
Kate makes two types of cake; chocolate(x) and carrot(y). She is able to bake 50 cakes at the most each week.
• It takes her 30 minutes to prepare each chocolate cake and 35 minutes to prepare each carrot cake.
• Kate has 1620 minutes [27 hours] available to prepare these cakes per week.
• She has a regular order for 12 chocolate and 10 carrot cakes each week that she must deliver.
• Kate makes a profit of $12 from each chocolate cake and $16 dollars from each carrot cake.
Q1
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.
Q2
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.
p
rofit
For Q1, I used these constraints x + y ≤ 50 , 0.5x + 0.58y ≤ 27, x ≥ 12, y ≥ 10 and the feasible region i got when i plotted the graph was(12,36.2) p=$723 (12,10) p=$304 and (40,10) p=$640 or is this the correct answer (12, 38)p= $736, (27.59, 22.41) p=$609.36 (50, 10) p=$680
• It takes her 30 minutes to prepare each chocolate cake and 35 minutes to prepare each carrot cake.
• Kate has 1620 minutes [27 hours] available to prepare these cakes per week.
• She has a regular order for 12 chocolate and 10 carrot cakes each week that she must deliver.
• Kate makes a profit of $12 from each chocolate cake and $16 dollars from each carrot cake.
Q1
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.
Q2
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.
p
rofit For Q1, I used these constraints x + y ≤ 50 , 0.5x + 0.58y ≤ 27, x ≥ 12, y ≥ 10 and the feasible region i got when i plotted the graph was(12,36.2) p=$723 (12,10) p=$304 and (40,10) p=$640 or is this the correct answer (12, 38)p= $736, (27.59, 22.41) p=$609.36 (50, 10) p=$680
