Question

: Sarah operates a concession stand at a downtown location throughout the year. One of her most popular items is circus peanuts, selling about 200 bags per month. Sarah pays $1 per bag. Sarah purchases the circus peanuts from Peter's Peanut Shop. She has been purchasing 100 bags at a time. To encourage larger purchases, Peter now is offering her discounts for larger orders according to the following price schedule. Discount Category Order Quantity Price per Bag 1 1 to 199 $1.00 2 200 to 499 $0.95 3 500 or more $0.90 Sara estimates an annual holding rate of 17% of the value of the peanuts. She also estimates an ordering cost of $4 for placing each order. Questions: 1-1 Sarah wants to decide which discounted price to adopt (if at all) and how much she should order. a. 200 b. 345 c. 354 d. 500 1-2 Only for the order-size that you answered in question 1, show how the total cost is calculated. (Show the values you substitute in the cost formulae; ordering cost, holding cost, purchasing cost). 1-3 Sarah knows she cannot stock more than 400 bags because of limited storage space. What would be her optimal ordering policy now? Use the template results. 200 b. 345 c. 354 d. 400

Answer 1

ANSWER:

1-1

For order quantity 1 to 199,

EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year)

=sqrt((2*200*12*4)/(1*17%)) = 336.0672202

As EOQ is not within this range so moving on to next range,

For order quantity 200-499,

EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year)

=sqrt((2*200*12*4)/(0.95*17%)) = 344.7976927

Total cost = ordering cost + holding cost + purchase cost = ((200*12)/344.7976927)*4 + (344.7976927/2)*(0.95*17%)+200*12*0.95 = 2335.684827

For order quantity 500 or more,

EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year)

=sqrt((2*200*12*4)/(0.9*17%)) = 354.2459542

But feasible quantity is adjusted upwards to 500 to avail the discounted

Total cost = ordering cost + holding cost + purchase cost = ((200*12)/500)*4 + (500/2)*(0.9*17%)+200*12*0.9 =2217.45

As the cost is lowest, discounted price to adopt is 0.9 and ordering quantity is d. 500 (Ans)

1-2
Total cost = ordering cost + holding cost + purchase cost = ((200*12)/500)*4 + (500/2)*(0.9*17%)+200*12*0.9 =2217.45

1-3.

With ordering quantity 400,

Total cost = ordering cost + holding cost + purchase cost = ((200*12)/400)*4 + (400/2)*(0.95*17%)+200*12*0.95 = 2336.3

As EOQ For order quantity 200-499 results in lower cost than ordering quantity 400,

Optimal ordering quantity = 344.7976927 = 345 (Rounded to nearest whole number)

So correct answer is b. 345

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