# 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...

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