You have

$2500

,

which can buy you a projection TV

($1600)

and a VCR

($900)

.

You plan to take them home with your own car. Due to the snowy weather

and your driving skill, the probability of having an accident is 0.5. When the

accident occurs, both TV and VCR will be totally damaged (i.e., their residual

values = zero). The transportation costs (money as well as time) are assumed

to be relatively minor and can therefore be ignored. For simplicity, assume that

your preference function is

U

=

√

w,

where w is the total value of these two

products.

(a) You can bring them home in one trip or in two separate trips. Which one

do you prefer?

(b) There is an insurance that you can purchase. The full coverage insurance

may cost you as much as

$1250

.

Are you better o

ff

in buying this insurance?

Draw a diagram to prove your assertion.

(c) The other option is to buy a partial coverage insurance. It pays 50 percent

of your losses at a cost of

$625

(half of what you pay under the full coverage

insurance). Compare this with the full coverage insurance and with no

insurance.

(d) The insurance company from which you purchase the insurance can go

bankrupt with a probability of 25%. Bankruptcy would make it impossible

for you to claim the loss, if incurred. What happens to your results above?

A modified Brayton cycle is to be analyzed using the air-standard assumption with constant specific heats at a temperature of 300K. Air flows through the Brayton cycle with a mass flow rate of 400 kg/s and enters the first compressor with a pressure of 100kPa and a density of 1.2 kg/m3.It is then compressed to 800kPa in the first of two compressors with an isentropic efficiency of 85%. After this compression, the air is cooled at constant pressure where it is now found to have a volumetric flow rate of 57.4 m3/s when it enters the second compressor. The second compressor has an isentropic efficiency of 85% as well and the air leaves this stage of the cycle at a pressure of 2.5 MPa.The cycle has a regenerator with an effectiveness of 75% which heats the air to a temperature of 600K after leaving the final compressor. The air enters the first turbine which has an isentropic efficiency of 90% at a temperature of 1200K after which it expands to a pressure of 700 kPa. The second and last turbine stage has an isentropic efficiency of 80%.Determine:a) The temperature of the air leaving the last turbineb) The net power production of the cyclec) The thermal efficiency of the cycle