A company is trying to decide whether or not to produce a ne

A company is trying to decide whether or not to produce a new electronic game. The fixed cost
(production, marketing, etc.) for the electronic game is $1,450,000. The company plans to sell the game
for $255. The unit (variable) cost for the game is uncertain and takes the following discrete distribution:
Cost     pro b.
100     0.20
105      0.25
110      0.30
115      0.15
120      0.10
First-year demand is uncertain but has a normal distribution with mean 11 = 11,000 units with a standard deviation a= 1500 units. Run a simulation for 1000 trials to determine first-year profit. First-year profit is given by: Profit= ($255- unit cost)* first-year demand- fixed cost.
a. Compute average first-year profit and standard deviation.
b. Determine the probability that the company will lose money (profit< 0).
c. Determine the probability that the company makes more than $200,000.

Solution

Simulation in Matlab:

prob=[0.20 0.25 0.30 0.15 0.10];
probcum= cumsum(prob);
cost=[100 105 110 115 120];
for i=1:1000
p(i)=int8(sum(rand>probcum)+1);
end
d=randn(1,1000)*1500+11000;
Profit= (255- cost(p)).*d- 1450000;

a.

mean(Profit)=1.62e5

std(Profit)=2.32e5

b.

mean(Profit<0)=0.256

c.

mean(Profit>200000)=0.45

Note that this is a simulation and you may get slightly different results if you run it.