1. Here is a linear demand function: 0.3Q = 12 – 3P. Find its price function by inverting the demand function. Then find its total revenue function by multiplying through by Q. EXAMPLE: The linear demand function Q = 400 -250P inverts into the price function P = 1.6 -0.004Q. Multiplying this by Q gives its total revenue function TR = 1.6Q -0.004Q2. This skill will be useful in assignment 4. Show the algebra involved.
a. Derive the price function from the demand function 0.3Q = 12 – 3P:
P= 4-0.1Q

b. Derive the total revenue function (TR) from your price function found in (a.):
TR = 4Q-0.1Q2

2. Evaluate the following TR function: TR = 4Q – 0.1Q2. EXAMPLE: When Q = 20, TR = $40.
a. When Q = 10, TR = $ b. When Q = 40, TR = $

3. Evaluate the following expression. Y = 5X2 +4X +6 EXAMPLE: When X = 2, Y = 34.

a. When X = 0, Y = ___ b. When X = 1, Y = ___
c. When X = 2, Y = ___ d. When X = 4, Y = ___

4. Evaluate the following exponentials. You may need to use a calculator with a Yx key. EXAMPLE: X -1/4. If X = 4, this gives _0.7071__. Compute to two decimal places or more.

a. X-1/5, When X = 2, this gives .
b. X1, When X = 4, this gives .
c. X1/2, When X = 64, this gives .
d. X3/4, When X = 2, this gives .

5. Find the two roots of each of the following functions (that is find the two X values that make Y = 0). This skill may be useful in assignment 11. EXAMPLE: Y = 3X2 -11X +6 is the product of (3X -2)(X -3). If you let Y = 3X-2 then X = 2/3 will make Y = 0. If you let Y = X-3 then X = 3 will make Y = 0. Thus both X = 2/3 and X = 3 are roots. Show the algebra involved.
a. Y = 4X2 +4X -8. The two roots are X = and X = .