Question

University Bakery makes three kinds of muffins – blueberry, banana nut, and chocolate chip. Demand for the three muffins are 20, 15 and 30 muffins per hour, respectively. University Bakery’s production process can produce any muffin at the rate of 90 muffins per hour but 0.5 hours are needed to switch between muffins. During those switchover times, the process doesn’t produce any muffins. The bakery wants to choose a production schedule that

(i) cycles repeatedly through the three muffins,
(ii) meets the required demand and
(iii) minimizes the amount of inventory held.

How many banana nut muffins should the bakery produce before switching over to another muffin?

Answer 1

To meet the demand of 15 muffins per hour, minimize inventory, and account for switchover times, University Bakery should produce 30 banana nut muffins before switching to another muffin type.

Step-by-step explanation:

The question relates to optimizing a bakery's production schedule to meet demand and minimize inventory. To calculate how many banana nut muffins the University Bakery should produce before switching over, we consider that the bakery can produce any muffin at the rate of 90 muffins per hour. Given the demand for banana nut muffins is 15 per hour, and taking the switchover time into account, we find a cycle that balances the production to meet demands across the three types of muffins.To ensure minimum inventory, the bakery must produce exactly what is needed for the demand within the cycle before switching over. Since the bakery produces 90 muffins an hour and we have a total demand for 20+15+30=65 muffins per hour, and considering 0.5 hours are lost in switching, the bakery can produce for only 2 hours in a 2.5-hour (3*0.5=1.5) cycle. This amounts to 180 muffins in a cycle. If we maintain the ratio according to the demand, we should produce a batch that includes 20 blueberry, 15 banana nut, and 30 chocolate chip muffins respectively per hour. Therefore, in a 2-hour production window before switchover, the bakery should make 40 blueberry, 30 banana nut, and 60 chocolate chip muffins. Hence, 30 banana nut muffins should be produced before the switchover.