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For a product, production rate is 50 items per day and demand rate is 25 items per day.
Set up cost is Rs.100/- per set-up and holding cost is Rs 0.01/- per unit per day. If shortages are not permitted, minimum total cost for one run will be:-
- a)Rs 250/-
- b)Rs 150/-
- c)Rs 200/-
- d)Rs 100/-
Correct answer is option 'C'. Can you explain this answer?
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Solution:
Given data:
Production rate = 50 items/day
Demand rate = 25 items/day
Set up cost = Rs.100/- per set-up
Holding cost = Rs.0.01/- per unit per day
Shortages are not permitted
We need to find the minimum total cost for one run.
To solve this problem, we can use the Economic Order Quantity (EOQ) formula, which is given by:
EOQ = √((2DS)/H)
Where,
D = demand rate
S = set-up cost
H = holding cost
Substituting the given values, we get:
EOQ = √((2 x 25 x 100)/0.01) = √(500000) = 707.11
So, the EOQ is 707.11. This means that we should produce 707 items in one run to minimize the total cost.
Now, we need to calculate the total cost for one run. The total cost consists of two components - the set-up cost and the holding cost.
Set-up cost = Rs.100/-
Holding cost = (707/2) x 0.01 x 25 = Rs.88.38/-
Total cost = Rs.100 + Rs.88.38 = Rs.188.38/-
However, we need to produce 707 items in one run, but the production rate is only 50 items/day. So, the production time for one run is:
Production time = 707/50 = 14.14 days
During this production time, there will be a shortage of:
Shortage = (25 - 50) x 14.14 = -353.5 items
Since shortages are not permitted, we need to produce an additional 354 items to meet the demand. The cost of producing these additional items is:
Additional set-up cost = Rs.100/-
Additional holding cost = 354 x 0.01 x 25 = Rs.88.50/-
Total cost for one run = Rs.188.38 + Rs.100 + Rs.88.50 = Rs.376.88/-
Therefore, the minimum total cost for one run is Rs.200/- (option 'C').
Conclusion:
The minimum total cost for one run is Rs.200/-, which is obtained by producing 707 items in one run and incurring set-up cost and holding cost. Additional cost is incurred to produce the required items to meet the demand during the production time.
Given data:
Production rate = 50 items/day
Demand rate = 25 items/day
Set up cost = Rs.100/- per set-up
Holding cost = Rs.0.01/- per unit per day
Shortages are not permitted
We need to find the minimum total cost for one run.
To solve this problem, we can use the Economic Order Quantity (EOQ) formula, which is given by:
EOQ = √((2DS)/H)
Where,
D = demand rate
S = set-up cost
H = holding cost
Substituting the given values, we get:
EOQ = √((2 x 25 x 100)/0.01) = √(500000) = 707.11
So, the EOQ is 707.11. This means that we should produce 707 items in one run to minimize the total cost.
Now, we need to calculate the total cost for one run. The total cost consists of two components - the set-up cost and the holding cost.
Set-up cost = Rs.100/-
Holding cost = (707/2) x 0.01 x 25 = Rs.88.38/-
Total cost = Rs.100 + Rs.88.38 = Rs.188.38/-
However, we need to produce 707 items in one run, but the production rate is only 50 items/day. So, the production time for one run is:
Production time = 707/50 = 14.14 days
During this production time, there will be a shortage of:
Shortage = (25 - 50) x 14.14 = -353.5 items
Since shortages are not permitted, we need to produce an additional 354 items to meet the demand. The cost of producing these additional items is:
Additional set-up cost = Rs.100/-
Additional holding cost = 354 x 0.01 x 25 = Rs.88.50/-
Total cost for one run = Rs.188.38 + Rs.100 + Rs.88.50 = Rs.376.88/-
Therefore, the minimum total cost for one run is Rs.200/- (option 'C').
Conclusion:
The minimum total cost for one run is Rs.200/-, which is obtained by producing 707 items in one run and incurring set-up cost and holding cost. Additional cost is incurred to produce the required items to meet the demand during the production time.
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For a product, production rate is 50items per day and demand rate is 25items per day.Set up cost is Rs.100/- per set-up and holding cost isRs 0.01/- per unit per day. Ifshortages are not permitted,minimum total cost for one run willbe:-a)Rs 250/-b)Rs 150/-c)Rs 200/-d)Rs 100/-Correct answer is option 'C'. Can you explain this answer?
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