Question 1

Solve each of the following pairs of simultaneous equations by elimination:

1. 3x +2y = 7

x + y = 3

1. 3x - 2y = 8

x + 4y = 26

1. X - y = 7

X + 2y = 16

1. 3y = 4x + 2

Y = -x + 10

Question 2

The total cost of making x units of a product is TC = 2x² + 4x + 500. What are the total, fixed, variable, marginal and average costs? What are the costs of making 500 units of the product?

Question 3

A small company produces two products, x and y. Product x requires 2 hour of labour and 12 tons of raw materials, whereas each unit of product y requires 4 hours of labour and 10 tons of raw material. The number of hours available each week is 80 and the available raw materials each week is 300 tons. If the contribution to profit is 4 per unit of product x and 6 per unit of y, determine the weekly production mix that will maximize profits.

Question 4

The totalrevenue and total cost for a product are related to production, x by:

TR = 14x - x² +2000

TC = x³ - 15x² + 1000

How many units should the company make to:

1. Maximize total revenue
2. Minimize total cost
3. Maximize profit

Question 5

John Lo thinks that the mean value of orders received by his firm is $260. He checks a sample of 36 accounts and finds a mean of $240 and standard deviation of $45. Does this evidence support his believe?