Assignment

Question 1

A drink manufacturer has monthly fixed cost of $24,000 and a production cost of $7 for each drink produced. The products sells for $10 per drink.

i. Derive the cost function?
ii. Derive the revenue function ?
iii. Derive the profit function?
iv. Calculate the profit (loss) corresponding to production leaves of 6,000 and 14, 000 drinks respectively.

Question 2

The profit function for a product is given by π(x) = -x3+98x2-700x-1800, where x is the number of units produced and sold. If break-even occurs when 10 units are produced and sold:

i. Find the quadratic factor of n(x)
ii. Find a number of units other than 10 that gives break - even for the product.

Question 3

The quantity demanded of a brand of food processors is 6000 per week when the unit price is $790 Every $40 change in price results in an inverse change in the quantity demanded by 500 units The suppliers will not market any food processors if the unit price $600 or less, but are willing to supply 5000 units per week at a unit price of $1050. If both the supply and demand curve are known to be linear.

i. Derive the demand curve
ii. Derive the supply curve
iii. Estimates the equilibrium quantity and price for food processors

Question 4

i. The profit for a product is given by π(x)=-1600+100x-x2, where x is the number of units produced and sold. How many units of the product must be sold to break even?

ii. Write the profit function in the form k -a(x-h)2

a. How many units of the product must be sold to maximise profit
b. What would the maximum profit be?