The national coffee store Farbucks needs to decide in August how many holiday insulated coffee mugs to order. Because the mugs are dated, those that are unsold by January 15 are considered a loss. These premium mugs sell for $23.95, and cost $6.75 each. Farbucks is uncertain of the demand. They believe that there is a 25% chance they will sell 10,000 mugs, a 50% chance they will sell 15,000, and a 25% chance they will sell 20,000. Build a decision tree to determine whether they should order 12,000, 15,000, or 18,000 mugs. Be sure that your model does not allow Farbucks to sell more mugs than it ordered: If demand is less than the order quantity, then the amount sold is the demand; otherwise, the amount sold is the order quantity.

If demand is less than the order quantity, then the amount sold is the demand; otherwise, the amount sold is the order quantity. This is showed in the calculation of the expected units sold.

Scenario 1: 12,000 units ordered

The cost is:

[tex]C=12,000*6.75=81,000[/tex]

The expected sales are:

[tex]Q_S=0.25*10,000+0.50*12,000+0.25*12,000\\\\Q_S=2,500+6,000+3,000\\\\Q_S=11,500\\\\\\S=Q_S*P=11,500*23.95=275,425[/tex]

Then, the profit becomes

[tex]R=S-C=275,425-81,000=194,425[/tex]

Scenario 2: 15,000 units ordered

The cost is:

[tex]C=15,000*6.75=101,250[/tex]

The expected sales are:

[tex]Q_S=0.25*10,000+0.50*15,000+0.25*15,000\\\\Q_S=2,500+7.500+3,750\\\\Q_S=13,750\\\\\\S=Q_S*P=13,750*23.95=329,312[/tex]

Then, the profit becomes

[tex]R=S-C=329,312-101,250=228,062[/tex]

Scenario 3: 18,000 units ordered

The cost is:

[tex]C=18,000*6.75=121,500[/tex]

The expected sales are:

[tex]Q_S=0.25*10,000+0.50*15,000+0.25*18,000\\\\Q_S=2,500+7,500+4,500\\\\Q_S=14,500\\\\\\S=Q_S*P=14,500*23.95=347,275[/tex]

Then, the profit becomes

[tex]R=S-C=347,275-121,500=225,775[/tex]

Units ordered Profit

12,000 $194,425

15,000 $228,062

18,000 $225,775

The decision tree is attached.

The calculations are the same as done here in the explanation.