Asked by ethan battista on May 09, 2024
Verified
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.
EOQ Analysis
Economic Order Quantity Analysis, a tool used in inventory management to determine the optimal order quantity that minimizes the total cost of inventory, including holding and ordering costs.
Carrying Costs
Expenses associated with maintaining inventory, including storage, insurance, and spoilage costs.
Ordering Costs
Expenses incurred in placing and receiving orders for goods, including transportation, handling, and clerical costs.
- Comprehend the Economic Order Quantity (EOQ) model and its application in reducing aggregate inventory expenditures.
- Compute the Economic Order Quantity and its associated total expense under diverse conditions, incorporating discounts and varied inventory frameworks.
- Examine the influence of inventory strategies on service standards and overall expenses.
Verified Answer
KF
Kimbryanna FinneyMay 14, 2024
Final Answer :
(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
(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
Learning Objectives
- Comprehend the Economic Order Quantity (EOQ) model and its application in reducing aggregate inventory expenditures.
- Compute the Economic Order Quantity and its associated total expense under diverse conditions, incorporating discounts and varied inventory frameworks.
- Examine the influence of inventory strategies on service standards and overall expenses.