Q1 Alex manages a chocolate store. His store sells two chocolates: the Swiss (S) and the Belgium (B) that are supplied by a manufacturer. The manufacturer charges a $200 fixed shipping and handling fee for each order of S or each order of B and the unit costs for S and B are $600 and $800, respectively. Demands for S and B are 250 per month and 300 per month, respectively. The inventory holding cost is based on an annual interest rate of 10%. Currently Alex manages his inventory by calculating the EOQ for each product separately. Assume that you can round the fractional order quantity to the nearest integer.
a) What are the EOQs for S and B? What are the annual setup and holding costs for S and B? (16 points)
b) Currently the store has a storage constraint that it can only hold 60 units of S and 75 units of B. What will be the optimal order quantities for S and B? What will be the resulting annual setup and holding costs? (Assume that the space for S cannot be used for B and vice versa.) (12 points)
Alex feels that calculating two separate EOQs is too cumbersome and he is considering ordering both S and B at the same time. That is whenever he places an order, he orders both S and B. The manufacturer charges a $400 shipping and handling fee for any sized order. Solve the following two parts based on this setting. Assume that there is no storage constraint.
c) Let T denote the time between successive orders. What will be the optimal T if Alex wants to minimize the total setup and holding cost? What are the corresponding order quantities? (6 points)
d) What is the resulting total annual setup and holding cost? How does it compare to the
cost in part (a) when Alex orders S and B separately? Explain the difference. (6 points)