Question 1168521
Let's solve this problem using the Economic Order Quantity (EOQ) model.

**1. Define Variables**

* D = Annual demand = 700 calculators
* H = Holding cost per unit per year = $2
* S = Ordering cost per order = $5 (fixed cost) + 2.35 * Q (where Q is the lot size)

**2. EOQ Formula**

The EOQ formula is:

EOQ = √(2DS / H)

However, we have an ordering cost that depends on the quantity, which is not the typical EOQ situation.

**3. Total Inventory Cost**

Total cost (TC) = Holding cost + Ordering cost

* Holding cost = (Q/2) * H = (Q/2) * 2 = Q
* Ordering cost = (D/Q) * S = (700/Q) * (5 + 2.35Q)

TC = Q + (700/Q) * (5 + 2.35Q)
TC = Q + 3500/Q + 1645

To minimize TC, we need to find the derivative of TC with respect to Q and set it to 0.

**4. Differentiate and Solve for Q**

* d(TC)/dQ = 1 - 3500/Q² = 0
* 1 = 3500/Q²
* Q² = 3500
* Q = √3500 ≈ 59.16

Since we must order whole calculators, we consider Q = 59 and Q = 60.

**5. Calculate Total Cost for Q = 59 and Q = 60**

* TC(59) = 59 + 3500/59 + 1645 ≈ 59 + 59.32 + 1645 ≈ 1763.32
* TC(60) = 60 + 3500/60 + 1645 ≈ 60 + 58.33 + 1645 ≈ 1763.33

Q = 59 minimizes the total cost.

**6. Calculate Number of Orders Per Year**

* Number of orders = D / Q = 700 / 59 ≈ 11.86

Since we can't have a fraction of an order, we round to 12.

**7. Final Answer**

The store should order 59 calculators 12 times per year to minimize inventory costs.