Starbucks needs to decide how many muffins and how many croissants to produce ea

Question

Starbucks needs to decide how many muffins and how many croissants to produce each day. The profit per muffin is $1 and the profit per croissant is $1.5. On an average, each muffin takes 3 minutes of labor time and 3 minutes of oven time (of course they are produced in batches. For simplification I have given you the time per piece). Croissants take 10 minutes of labor time and 1 minute of oven time. Starbucks can have its labor dedicated for a maximum of 2 hours every day. The oven time is limited to 6 hours during the night. Due to customer requests Starbucks produces at least 5 croissants every day. Which of the following statements are TRUE (choose all the correct statements. Choosing wrong answers will incur negative marking) Producing 10 muffins and 8 croissants in a day is feasible but worse than producing 15 muffins and 6 croissants a day. Producing 10 muffins and 8 croissants in a day is feasible AND better than producing 15 muffins and 6 croissants a day. Producing 10 each of muffins and croissants is feasible and the corresponding profit is $25. Producing 10 each of muffins and croissants is infeasible The profit from producing 5 croissants and 5 muffins is $10 The profit from producing 5 croissants and 5 muffins is $12.5

Explanation / Answer

Profit-Muffins= 1$ and Profit croissants= 1.5$ Table below gives the muffin and croissants labour and oven time

Contraints:

Labor Time = 2 hours or 120 minutes

Oven Time= 6 hours or 720 minutes

Minimum 5 croissants to be made

Statement 1: Producing 10 muffins and 8 croissants is feasible but worse than producing 15 muffins and 6 croissants a day.

(10M+8C)Labour= 10*3 + 8*10 = 30+80 = 110minutes(within constraint)

(10M+8C)Oven = 10*3 + 8*1 = 30+8 = 38minutes(within constraint)

Therefore Profit= 10*1+8*1.5= 10+12= 22$

(15M+6C)Labour= 15*3 + 6*10 = 45+60 = 105minutes(within constraint)

(15M+6C)Oven = 15*3 + 6*1 = 45+6 = 51minutes(within constraint)

Therefore Profit= 15*1+6*1.5= 15+9= 24$

Therefore we see that both are feasible, but 10 Muffins+8 croissants are worse in terms of profit in comparison to 15 Muffins and 6 croissants. Statement 1 is TRUE.

Statement 2: Producing 10 muffins and 8 croissants is feasible AND better than producing 15 muffins and 6 croissants a day. From the result of (1), we know that this statement is FALSE.

Statement 3: Producing 10 each of muffins and croissants is feasible and the corresponding profit is 25$

(10M+10C)Labour= 10*3 + 10*10 = 30+100 = 130minutes(crosses constraint)

(10M+8C)Oven = 10*3 + 10*1 = 30+10 = 40minutes(within constraint)

Therefore Profit= 10*1+10*1.5= 10+12= 25$

Although the profit value is correct it is not feasible to run this as it crosses the labour constraint. Statement 3 is FALSE.

Statement 4: Producing 10 each of muffins and croissants is infeasible.

This statement is TRUE as per the result from statement 3.

Statement 5: The profit from producing 5 croissants and 5 muffins is 10$

The profit = 5*1 + 5*1.5 = 5+7.5 = 12.5$

Statement 5 is FALSE as the profit is 12.5$

Statement 6:The profit from producing 5 croissants and 5 muffins is 10$

The profit = 5*1 + 5*1.5 = 5+7.5 = 12.5$

Statement 5 is TRUE as the profit is 12.5$

Therefor statements 1,4&6 are TRUE. Please tick them.

Muffins Croissants Labour Time 3 minutes 10 minutes Oven Time 3 minutes 1 minute

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