Exercise 2 | Wiskunde op Tilburg University

Shop A and B are neighbors and both sell calculators. The annual demand in shop A is 20, the annual demand in shop B is 45. The order costs are 10 for both shops and the annual holding costs per calculator are 1 euro for both shops. Currently, they each place their own individual orders. They consider placing orders together. Calculate the total savings (round to cents) if they decide to do that.

Antwoord 1 correct

Correct

Antwoord 2 optie

11.76

Antwoord 2 correct

Fout

Antwoord 3 optie

4.66

Antwoord 3 correct

Fout

Antwoord 4 optie

Antwoord 4 correct

Fout

Antwoord 1 optie

13.94

Antwoord 1 feedback

Correct:

$q_A=\sqrt{\dfrac{2\cdot 10 \cdot 20}{1}}=20$ and

$q_B=\sqrt{\dfrac{2\cdot 10 \cdot 45}{1}}=30$ .

Therefore,

$TC_A(20)=\dfrac{10 \cdot 20}{20}+\dfrac{1\cdot 20}{2}=20$ and

$TC_B(30)=\dfrac{10 \cdot 45}{30}+\dfrac{1\cdot 30}{2}=30$ , which gives a total cost of

$50$ .

If shop A and B cooperate, then

$q=\sqrt{\dfrac{2\cdot 10 \cdot 65}{1}}=\sqrt{1300}$ . Then

$TC(\sqrt{1300})=\dfrac{10 \cdot 65}{\sqrt{1300}}+\dfrac{1\cdot \sqrt{1300}}{2}=36.06$ (rounded to cents).

Hence, the total savings are

$50-36.06=13.94$ .

Go on.

Antwoord 2 feedback

Wrong: When shop A and B order together the annual holding costs remain 1 euro per calculator. Moreover, the order costs remain 10 euro.

Try again.

Antwoord 3 feedback

Wrong: The optimal order quantity is not

$q=\sqrt{\dfrac{cd}{h}}$ .

See Inventory management.

Antwoord 4 feedback

Wrong: These two shops can indeed save some costs by cooperating.

Try again.