PRODUCTION MANAGEMENT II (QUANTITY DISCOUNT MODEL) ILLUSTRATION

 

Emma and the rest of the class reps are considering organizing a dinner/award night for CDL business Administration Students for the year 2015 set.

The demand from the students is 10,000 units of awards, the quantity Emma is considering producing  is unknown, but the ordering cost by the students is N200.  The cost for producing one award is N50,000, due to the high cost of the ticket of 10% discount. 

As a potential manager, you are required to calculate:

i.                    Total Cost that will take to organize

ii.                  The optimum quantity of award each student is expected to go home  

SOLUTION:

First of all, let’s take a look at the formula:

(1)               TC =   DC   + DCo  + QCc

            Q         2

(2)               Q^opt = √2DC

              CI

Note:  CI; the I is the percentage while the C is the cost.  This is the same as carrying cost                

Now let’s solve:

Bring out the variables first:

D= 10,000

Co = 200

Cost of production is N50,000

I = 10%

Q^opt = √2DC

CI

Q^opt = √(2)(10,000) (50,000)

(50,000 (10%)

Let me explain here; from the top we have (2).  That (2) is constant in the question.  Then we have D which we have substituted to (10,000).  That D is the demand in the question.  Then We have C which we substituted to (50,000). The C is the cost.

When you come do, where we have CI, the C is still the 50,000 which is the cost while the I is the percentage which is 10%.  This 10% is in the question.

With this explanation, we can continue from where we stop.

 Q^opt = √1,000,000,000

                5,000

Q^opt = √200,000

Q^opt = 447 units

That is it.  Use your calculator and you will arrive at the same answer.

Now let’s work for the Total Cost which is the TC:

Here is the formula:

TC =   DC   + DCo  + QCc

            Q         2

All we need to do is to substitute the figures:

TC =   (10,000) (50,000)   + (10,000) (200)  + (447)(50,000)

                447                            2

TC =   1,118,568.23   + 1,000,000  + 2,235,000

                                          

TC =   14,353,568.28

                                          

Note that we work on quantity first because we need it to solve for the total cost.  Since, we don’t have quantity given to us in the question, we have to solve for it to get the figure so that to enable us work for TC (Total Cost).

Please, do contact me if you are confuse; theotherwomaninmarriage@gmail.com