1. The demand for an economics textbook is given by:

Q = 673 - 3p²

Find the value of Q1 when demand is unit elastic and hence calculate the new price (rounded to two decimal positions) needed to increase Q by 100 units from the Q1 value.

Note: Express the new price with two decimal positions (avoid intermediate roundings in the calculation process).

2.

The demand for concert tickets is given by:

Q = 53625 / (p² - 71)

where Q is measured in thousands of tickets.

Considering the value of the price elasticity of demand at P= 95, calculate the percentage change in Q due to an 8% increase in price (with respect to P=95).

Note: Round your answer to two decimal positions. Positive percentage indicates increase of the magnitude, negative percentage indicates decrease of the magnitude.

3.

Assume that the total revenue received from the sale of x items is given by, R(x)= 26 In(6x + 2), while the total cost to produce x items is C(x)= x / 2.

Find the number of items that should be manufactured so that profit, R(x) - C(x), is a maximum.

Note: round the result to 2 decimal positions.