  I need a detailed assistance to solve this problem in: Operations Analysis.3) A chemical manufacturer produces a compound at the rate of 10,000 pounds a day over 250 days each year.  Annual demand for that compound is 600,000 pounds per year, and each pound sells for \$3.90.  There is a fixed setup cost of \$1,500 for each production run, and a variable cost of \$3.50 for each pound produced.  The following costs are incurred:Interest rate on the cost of capital is 22% per annum (annually).Storage and handling costs amount to 12% of the compounds cost per annum.a)- What is the optimal production lot for the compound (write down the model name, its parameters and formula)?b)- Compute the uptime, downtime and cycle time in days, and find the cycle fraction of uptime and the cycle fraction of downtime (include the formula). c)-  What are average annual holding and setup costs for the compound (include the formula)?d) - What is the annual profit for this compound?

Question

I need a detailed assistance to solve this problem in: Operations Analysis.

3) A chemical manufacturer produces a compound at the rate of 10,000 pounds a day over 250 days each year.  Annual demand for that compound is 600,000 pounds per year, and each pound sells for \$3.90.  There is a fixed setup cost of \$1,500 for each production run, and a variable cost of \$3.50 for each pound produced.  The following costs are incurred:

• Interest rate on the cost of capital is 22% per annum (annually).
• Storage and handling costs amount to 12% of the compounds cost per annum.
• a)- What is the optimal production lot for the compound (write down the model name, its parameters and formula)?

• b)- Compute the uptime, downtime and cycle time in days, and find the cycle fraction of uptime and the cycle fraction of downtime (include the formula).
• c)-  What are average annual holding and setup costs for the compound (include the formula)?
• d) - What is the annual profit for this compound?
Step 1

Step1: Calculating the value of optimal production lot for the compound. We have,

Model Name: Economic production Quantity (EPQ)

The formula of EPQ is as follow:

EPQ = Square Root of [2 x D x S / h (1- D/P)]

Here,

D = Annual Demand = 600,000 pounds per year

S = Set-up Cost per production run = \$ 1,500

P = Total production = 10,000 x 250 = 2,500,000

h =Holding cost = (Cost of capital + Storage and handling cost) Variable cost per pound

h = (0.22 + 0.12) \$ 3.50 = 0.32 x \$ 3.50 = \$ 1.12 per pound, per year

Substituting these value in the above formula. We get;

EPQ = Square Root of [2 x 600,000 x \$1,500 / \$ 1.12 (1- 600,000/2,500,000)]

EPQ = Square Root of [\$1,800,000,000 / \$ 1.12(1 – 0.24)]

EPQ = 45,985.45 units

Step 2

Step2: Calculating the value of uptime, downtime and cycle time in days, cycle fraction of uptime and the cycle fraction of downtime. We have,

(a)  Cycle time between production run = EQP / Total Demand

Time between production run = 45,985.45 / 600,000

Time between production run = 0.07664

(b) Value of uptime = EPQ / Total production

Value of uptime = 45,985.45 / 2,500,000

Value of uptime = 0.01839

(c) Value of downtime = Cycle time between production run – Value of uptime

Value of downtime = 0.07664 – 0.01839

Value of downtime = 0.05825

(d) Cycle fraction of uptime = Value of uptime / Cycle time between production run

Cycle fraction of uptime = 0.01839 / 0.07664

Cycle fraction of uptime = 0.2399

(e) Cycle fraction of downtime = Value of downtime / Cycle time between production run

Cycle fraction of downtime = 0.05825 / 0.07664

Cycle fraction of downtime = 0.760

Step 3

Step3: Calculating the value of average annual holding and setup costs for the compound. We have,

The average annual cost of holding and setup = D*S/Q + h (1- D/P) Q/2

Here,

D = Total Demand = 600,000 pounds

P = Total production = 2,500,000

S = Set-up cost = \$ 1,500

Q = EPQ = 45,985.45 pounds

h = Carrying cost = = (0.22 + 0.12) \$ 3.50 = 0.32 x \$ 3.50 = \$ 1.12 per pound, pe...

Want to see the full answer?

See Solution

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in 