Question

with the steps of the solution

d. 17.5 marks] A remotely situated fuel cell has an installed cost of $2,000 and will reduce existing surveillance expenses by $350 per year. The border security agency's MARR is 10%. What is the approximate minimum useful life that makes the fuel cell purchase break even? i. 8.52 ii. 8.63 iii. 8.77 iv. 8.89 e. [7.5 marks] The production rate of a company (D) could be 100 units per year with a probability of 0.4 or 125 units per year with a probability of 0.6. Moreover, the profit per unit sold (S) is either $5 with a probability of 0.35 or $7 with a probability of 0.65. What are the expected value and the standard deviation of the total annual profit (P)? i. 724.5 and 132 ii. 724.5 and 134.6 iii. 832.5 and 98.7 iv. 924.8 and 110.5

Answer 1

Part (D)

2000 = 350,10%, n) A 2000 10% = 5.7142 350

$at\ n=8.889322\\ (\frac{P}{A},10\%,n)=5.71405$

correct answer is (D) 8.89

Part (E)

$if\ X\ is\ a\ random\ variable\\ expected\ value,E(X)=\sum{x*p(x)}\\ variance,var(X)=E(X^{2})-[E(X)]^{2}=\sum{x^{2}*p(x)}-[\sum{x*p(x)}]^{2}\\$

variance of production rate = (1002 *0.4+ 1252 *0.6) – 1152 = 4000+ 9375 – 13225 150

$var(XY)=(\sigma_{X}^{2}+[E(X)]^{2})*(\sigma_{Y}^{2}+[E(Y)]^{2})-[E(X)]^{2}*[E(Y)]^{2}\\$

correct answer is (B)