Answer:
The owner's total profit is $120,000.
Step-by-step explanation:
Assume that:
X₁ = contract is assigned to firm 1
X₂ = contract is assigned to firm 2
The sample space for assigning the two contracts is:
S = {(I, I), (I, II), (I, III), (II, I), (II, II), (II, III), (III, I), (III, II) and (III, III)}
There are total of 9 possible combinations.
So, the probability of selecting any of the combination is, 1/9.
Compute the probability distribution of X₁ and X₂ as follows:
X₁ P (X₁) X₂ P (X₂)
0 4/9 0 4/9
1 4/9 1 4/9
2 1/9 2 1/9
Compute the expected values of X₁ and X₂ as follows:
[tex]E(X_{1})=\sum X_{1}\cdot P(X_{1})\\\\=(0\times\frac{4}{9})+(1\times\frac{4}{9})+(2\times\frac{1}{9})\\\\=\frac{6}{9}\\\\=\frac{2}{3}[/tex] [tex]E(X_{2})=\sum X_{2}\cdot P(X_{2})\\\\=(0\times\frac{4}{9})+(1\times\frac{4}{9})+(2\times\frac{1}{9})\\\\=\frac{6}{9}\\\\=\frac{2}{3}[/tex]
It is provided that each contract will yield a profit of $90,000.
Compute the owner's total profit as follows:
[tex]\text{Total Profit}=\text{Profit}\times [E(X_{1})+E(X_{2})][/tex]
[tex]=90000\times[\frac{2}{3}+\frac{2}{3}]\\\\=120000[/tex]
Thus, the owner's total profit is $120,000.
