KF
Answered
Clement Bait and Tackle has been buying a chemical water conditioner for its bait (to help keep its baitfish alive) in an optimal fashion using EOQ analysis. The supplier has now offered Clement a discount of $0.50 off all units if the firm will make its purchases monthly or $1.00 off if the firm will make its purchases quarterly. Current data for the problem are: D = 720 units per year; S = $6.00, I = 20% per year; P = $25.
a. What is the EOQ at the current behaviour?
b. What is the annual total cost, including product cost, of continuing their current behaviour?
c. What are the annual total costs, if they accept either of the proposed discounts?
d. At the cheapest of the total costs, are carrying costs equal to ordering costs? Explain.
On May 14, 2024
(a) Q∗ = 2⋅720⋅62⋅25\sqrt { \frac { 2 \cdot 720 \cdot 6 } { 2 \cdot 25 } }2⋅252⋅720⋅6 = 41.57 or 42 units at a time.
(b) TC = 720 ∙ 25 + 72041.57\frac { 720 } { 41.57 }41.57720 ∙ 6 + 41.572\frac { 41.57 } { 2 }241.57 ∙ .2 ∙ 25 = 18000 + 103.92 = 103.92 + $18,207.85
(c) Placing orders on a monthly basis implies twelve orders per year where Q = 720 / 12 = 60. Placing orders on a quarterly basis implies four orders per year where Q = 720/4 = 180.
(d) They are not; accepting the discount requires an order quantity that is not EOQ. Purchasing 42 units at a time led to setup costs and holding costs of $104 each. With the more favorable discount, setup costs are $24 while holding costs are $432.
Range 1 Range 2 Range 3 Quantity 1−5960−179179+ Unit Price, P $25$24.5$24 Q* (Square root formula) 41.5741.9942.43 Order Quantity 41.5760180 Holding cost 103.927224 Setup cost 103.93147432 Product cost 18,000.0017,640‾17,280‾ Total cost, TC$18,207.85$17,859$17,736\begin{array} { | l | c | c | c | } \hline & \text { Range 1 } & \text { Range 2 } & \text { Range 3 } \\\hline \text { Quantity } & 1 - 59 & 60 - 179 & 179 + \\\hline \text { Unit Price, P } & \$ 25 & \$ 24.5 & \$ 24 \\\hline & & & \\\hline \text { Q* (Square root formula) } & 41.57 & 41.99 & 42.43 \\\hline \text { Order Quantity } & 41.57 & 60 & 180 \\\hline & & & \\\hline \text { Holding cost } & 103.92 & 72 & 24 \\\hline \text { Setup cost } & 103.93 & 147 & 432 \\\hline \text { Product cost } & 18,000.00 & \underline { 17,640 } & \underline { 17,280 } \\\hline \text { Total cost, } T _ { C } & \$ 18,207.85 & \$ 17,859 & \$ 17,736 \\\hline\end{array} Quantity Unit Price, P Q* (Square root formula) Order Quantity Holding cost Setup cost Product cost Total cost, TC Range 1 1−59$2541.5741.57103.92103.9318,000.00$18,207.85 Range 2 60−179$24.541.99607214717,640$17,859 Range 3 179+$2442.431802443217,280$17,736