Question

At the beginning of December, XYZ Company employed a contractor to cut enough trees to meet the expected demand for Christmas trees. They sell these trees to a local wholesaler in batches of 100. Over the past few years, the demand has been as follows, Demand Probability 0 0% 1 4% 2 6% 3 10% 4 23% 5 17% 6 14% 7 12% 90% 57% None of above 96% 80% 8 9% 9 5%

If it costs $12 to cut and trim a tree that sells for $28, how many trees should the company cut down?

What is the profit (loss) if the company decides to cut 400 trees, and the demand is 200?

What is the expected profit (loss) if the company decides to cut 400 trees?

Answer 1

If the company decides to cut 400 trees, then the cost incurred is 400*12 = 4800. However, they will only be able to sell 200 trees. So the revenue earned is 200*28 = 5600. This means the profit is 5600-4800 = $800

If the company decides to cut 400 trees we can calculate the expected profit using EMV formula. If the company decides to cut 400 trees and the demand is less than 400 then there will certain loss. However if the demand is 400 or more then the profit is capped. That is 400*(28-12) = 6400

If the demand is 0 then the expected profit is -400*12 = -4800

If the demand is 100 then the expected profit is -400*12 + 100*28 = -2000

If the demand is 200 then the expected profit is -400*12 + 200*28 = 800

If the demand is 300 then the expected profit is -400*12 + 300*28 = 3600

We can create the payoff table as shown below

Demand	Probability	Payoff at 400
0	0%	-4800
1	4%	-2000
2	6%	800
3	10%	3600
4	23%	6400
5	17%	6400
6	14%	6400
7	12%	6400
8	9%	6400
9	5%	6400

The sum product of probability and payoff is 0% of (-4800) + 4% of (-2000) + 6% of 800 + 10% of 3600 + … + 9% of 6400 + 5% of 6400 = 5448

The expected profit if the company decides to cut 400 trees is $5448