Question 5

A firm has the following linear total revenue 𝑅(𝑥) and total cost 𝐶(𝑥) functions. • 𝑅(𝑥) = 55𝑥

[4 marks]

• 𝐶(𝑥)=30𝑥+250

Find the break-even point for the firms.

Hint:

(1) find the profit function, setting it equal to zero, and solving for 𝑥, (2) setting 𝑅(𝑥) = 𝐶(𝑥) and solving for 𝑥, and
(3) graphing 𝑅(𝑥) and 𝐶(𝑥) and find the point of intersection.

3. In all of this question let q> 0 represent quantity (i.e. number of units) and p > 0 represent unit price (i.e. price per unit). Assume a demand function p = and an average cost 1 100 function cq) = + (a) Given that "profit = revenue - cost" find the profit function, F(q). [4 points) (b) Find the value of q that maximizes total profit and state the maximum profit. Sufficiently justify that your value actually maximizes the total profit function. [9 points) (c) Verify that "marginal revenue" = "marginal cost" at the value of q that maximizes total profit. [3 points)

2 , 37. Find the point of intersection of the line (2, y, z) = (2, -1, 4) + t(1,2, -1) with the plane marks 3.r +y - 2 = 31. Show your work.

Find the point of intersection 
X+2y=3 
5x+4y=8