A consumer's demands x, y for two different goods are chosen to maximize the

utility function

(, ) = + (x 0, y 0)

subject to the budget constraint + = (where p, q, m > 0)

(d) Find the utility-maximizing demands for both goods, as well as the Lagrange

multiplier , all as functions of the three variables (p, q, m).

2.Find the general solution of the differential equation dy/dt=t^4.

Also find the solutions which satisfy y=1 when t=0 and y=0 when t=1 and sketch them on the same axes.

3.Show that the function x^2-2xy+5y^2-10x+2y is convex. Find its global minimum value.

4.If the government withdraws the funding for abortion services through Planned Parenthood, what impact would this have on the market for abortion services in the united states? What do you think people will do?

5.a car was bought on installment basis with a monthly payment of $10000 for 60 months. If the interest rate is 12% compounded annually,calculate the cash price

6.Suppose the Sunglasses Hut Company's profit is given by the equation P=-0.02q²+3q-32,where P is the total profit, in thousands of dollars, and q is the total number of sunglasses sold, in thousands. For example, when q=10, the equation says that P=-4. This would mean that when 10000 sunglasses are sold, the profit is $-4000.

How many pairs of sunglasses (in thousands) should be sold to maximize profits?

Answer: ?

thousand pairs of sunglasses need to be sold.

What are the actual maximum profits (in thousands) that can be expected?

7.In what way could tax policy be used to slow a rapidly growing economy?

8.if you paid $89 to a loan company for the use of $1075 for 82 days, what annual rate of interest did they charge? (Assume a 360-day year)

9.The profit in dollars of the sale of x expensive watches is P(x)=0.03x^2-3x-6x^0.4-4000. Find for x=400, x=2000,x=5000, x=10000

10.Using properly labelled diagrams illustrate what will happen to the equilibrium price and quantity of muesli (ceteris paribus), in the following scenarios

Research has shown that muesli is good for the heart