Write down the equation of a utility function and construct an indifference map that corresponds to each of the following case: -Bob always consumes beer and pizza in fixed proportions. Specifically, If Bob has 1 pizza, he consumes precisely 2 beers and additional beers represent no additional utility for Bob. Similarly, if Bob has 2 beers, he consumes precisely 1 pizza and additional pizzas represent no additional utility for Bob. In addition, when Bob has 4 pizzas and 10 beers, his utility is 32. **I understand that the formula for utility for perfect compliments is U(x,y)=min(aX,bY). How do you get the values a and b??? What do a and b represent in the equation??

In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.44 m. The mug slides off the counter and strikes the floor 1.60 m from the base of the counter.

(a) With what velocity did the mug leave the counter?

(b) What was the direction of the mug's velocity just before it hit the floor?​ ° (below the horizontal)​

Write down the conservation of energy equation for heat when a mass of ice, at a temperature less than 0℃ (T1), is added to a copper (Cu) container holding some hot water, at a temperature less than 100℃ (T2) . Underneath each term indicate the process involved, e.g. ice warms (Q1), ice melts (Q2), water that was ice warms (Q3), hot water cools (Q4), copper container cools (Q5). Your equation must contain all these variables mice,mwater,mCu,cice, cwater, cCu and Lf; the initial temperatures T1 and T2; and the final equilibrium temperature T3.

The buyer of a piece of real estate is often given the option of buying down the loan. This option gives the buyer a choice of loan terms in which various combinations of interest rates and discount points are offered. The choice of how many points and what rate is optimal is often a matter of how long the buyer intends to keep the property.

Darrell Frye is planning to buy an office building at a cost of $988,000. He must pay 10% down and has a choice of financing terms. He can select from a 7% 30-year loan and pay 4 discount points, a 7.25% 30-year loan and pay 3 discount points, or a 7.5% 30-year loan and pay 2 discount points. Darrell expects to hold the building for four years and then sell it. Except for the three rate and discount point combinations, all other costs of purchasing and selling are fixed and identical.

1. What is the amount being financed?

2. If Darrell chooses the 4-point 7% loan, what will be his total outlay in points and payments after 48 months?

3. If Darrell chooses the 3-point 7.25% loan, what will be his total outlay in points and payments after 48 months?

4. If Darrell chooses the 2-point 7.5% loan, what will be his total outlay in points and payments after 48 months?

5. Of the three choices for a loan, which results in the lowest total outlay for Darrell?

1. You are ready to buy a house and you have $50,000 for a down payment and closing costs. Closing costs are estimated to be 2.5% of the loan value.   You have an annual salary of $200,000. The bank is willing to allow your housing costs – mortgage, property tax and homeowners insurance to be equal to 28% of your monthly income. You have estimated that property tax will be $1,000/month and homeowner’s insurance will be $100/month. The interest rate on the loan is 3.4% per year with monthly compounding for a 30-year fixed rate loan.
   1. How much money will the bank loan you?
   2. How much can you offer for the house?
   3. Create a loan amortization table in Excel and submit the spreadsheet. This should be done with monthly payments.

What determines the value of a bond? Write down the formula for determining the price of the bond and explain it briefly?

When performing a CVP Analysis, it is important to break down costs into

a) Product and Period costs

b) Prime and Conversion costs

c) Fixed and Variable costs

d) Fixed, Mixed and Variable costs

Neutrons are born out of fission at a high energy and must be slowed down to the low energy region, called the “thermal energy” region, to cause another fission. A material called a “moderator” is used to slow the neutrons down, or “moderate” them, by elastic scattering collisions.The average neutron energy coming out of fission of thermal neutrons is 1.98 MeV in kinetic energy. What is the number of collisions required to bring its average kinetic energy to 0.1 eV if it elastically scatters off of the following moderators:

a. Hydrogen-1

b. Hydrogen-2

c. Carbon-12

d. Uranium-238

The cart rolls down an incline. The launcher fires the ball in a direction perpendicular to the cart. Show that the ball lands back in the cart.