Mastering Mathematical Techniques: MTH601 Assignment #1 solution for Spring 2023

MTH601 Assignment #1 solution for Spring 2023 

Description: Get ready to ace your MTH601 assignment with our comprehensive guide for Spring 2023. Explore essential mathematical techniques and concepts covered in this assignment. Learn from expert instructor Lubna Mustafa as you work towards the due date of 2nd June 2023. Boost your understanding of 1-6 lectures, consolidate your knowledge, and solve assignment questions with confidence. Follow our instructions to submit your assignment via LMS and ensure a successful submission. Don't miss this opportunity to excel in MTH601 and strengthen your mathematical skills.

MTH601 Assignment #1 solution for Spring 2023 

Question 1 Solution: (a) The economic order quantity (EOQ) can be calculated using the EOQ formula: EOQ = √((2 * Demand * Ordering cost) / Holding cost) Given: Demand rate = 24000 units/year Ordering cost = Rs. 300/order Holding cost = Rs. 0.20/item/month

First, convert the holding cost to a yearly basis: Holding cost = Rs. 0.20/item/month * 12 months/year = Rs. 2.40/item/year

Now, substitute the values into the formula: EOQ = √((2 * 24000 * 300) / 2.40) EOQ = √(14400000 / 2.40) EOQ = √6000000 EOQ ≈ 2449 units

Therefore, the economic order quantity is approximately 2449 units.

(b) The time between orders can be calculated using the EOQ: Time between orders = EOQ / Demand rate Time between orders = 2449 units / 24000 units/year Time between orders ≈ 0.102 years

Therefore, the time between orders is approximately 0.102 years.

(c) The number of orders per year can be calculated as the inverse of the time between orders: Number of orders per year = 1 / Time between orders Number of orders per year ≈ 1 / 0.102 Number of orders per year ≈ 9.804

Therefore, the number of orders per year is approximately 9.804, which can be rounded to 10 orders per year.

(d) The optimum annual cost can be calculated by substituting the EOQ into the total cost formula: Total cost = (Demand * Ordering cost) / EOQ + (EOQ * Holding cost) / 2 Total cost = (24000 * 300) / 2449 + (2449 * 2.40) / 2 Total cost = 7200000 / 2449 + 2937.6 / 2 Total cost ≈ 2942.46 + 1468.8 Total cost ≈ Rs. 4411.26

Therefore, the optimum annual cost is approximately Rs. 4411.26.

Question 2 Solution: (a) The optimum order quantity can be calculated using the EOQ formula: EOQ = √((2 * Demand * Ordering cost) / Holding cost) Given: Demand rate = 20000 units/year Ordering cost = Rs. 500/order Holding cost = Rs. 1.4/unit/year

Substitute the values into the formula: EOQ = √((2 * 20000 * 500) / 1.4) EOQ = √(20000000 / 1.4) EOQ = √14285714.29 EOQ ≈ 3780 units

Therefore, the optimum order quantity is approximately 3780 units.

(b) The time between orders can be calculated using the EOQ: Time between orders = EOQ / Demand rate Time between orders = 3780 units / 20000 units/year Time between orders ≈ 0.189 years

Therefore, the time between orders is approximately 0.189 years.

(c) The number of orders per year can be calculated as the inverse of the time between orders: Number of orders per year = 1 / Time between orders Number of orders per year ≈ 1 / 0.189 Number of orders per year ≈ 5.291

Therefore, the number of orders per year is approximately 5.291, which can be rounded to 5 orders per year.

(d) The optimum shortages can be calculated using the formula: Shortages = (Demand - EOQ) * Shortage cost Given: Demand rate = 20000 units/year EOQ ≈ 3780 units Shortage cost = Rs. 6/unit/year

Substitute the values into the formula: Shortages = (20000 - 3780) * 6 Shortages = 16220 * 6 Shortages = Rs. 97,320

Therefore, the optimum shortages amount to Rs. 97,320 per year.