Download Self Assessment Quadratic Equations 1. Determine whether

Self Assessment
Quadratic Equations
1.
Determine whether solutions exist for each of the following quadratic equations.
Where they do find the solution(s).
(i)
(ii)
x2 − 2x = 0
(3x − 6)(x + 1) = 0
(iii)
(iv)
(v)
(vi)
9 x 2 − 24 x + 16 = 0
3x 2 + 2 x + 3 = 0
2 x 2 + 11x − 21 = 0
− 2 x 2 + x + 10 = 0
2. A firms demand function for a good is given by P = 107-2Q and their total
cost function is given by TC = 200+3Q .
(i)
Obtain an expression for total revenue (price X quantity) in terms of Q
(ii)
For what values of Q does the firm breakeven (Note: Break even where
Profit = 0 or TR=TC)
Illustrate the answer to (ii) using sketches of the total cost function, the
total revenue function and the profit function
From the graph estimate the maximum profit and the level of output for
which profit is maximised
(iii)
(iv)
3. What is the profit maximising level of output for a firm with the marginal cost
function MC = 1.6Q2-15Q+60 and a marginal revenue function MR = 280-20Q?
Note: Profit is maximised where MR=MC
4. The demand function for a good is given as Q = 130-10P. Fixed costs associated
with producing that good are €60 and each unit produced costs an extra €4.
(i)
(ii)
(iii)
(iv)
Obtain an expression for total revenue and total costs in terms of Q
For what values of Q does the firm break even
Obtain an expression for profit in terms of Q and sketch its graph
Use the graph to confirm your answer to (ii) and to estimate maximum
profit and the level of output for which profit is maximised