ANSWER ALL THE QUESTIONS

1. Suppliers of bicycles will make 200 bicycles available in the market per month when the unit price is Sh.50 and 2000 bicycles available per month when the unit price is Sh.100. Find the supplier equation if it is known to be linear. [2 Marks]
2. The cost function and the revenue function for a certain firm are given by C(x) = 12x + 20,000 and R(x) = 20x, respectively. Find the break-even point for the company. [2 Marks]
3. Given the demand equation 3x + p - 40 = 0 and the supply equation 2x - p + 10 = 0, where p is the unit price in dollars and x represents the quantity in units of a thousand, determine the equilibrium quantity and the equilibrium price. [2 Marks]
4. A farmer has 200 acres of land suitable for cultivating crops A, B and C. the cost of cultivating crops A, B and C is Sh.40 per acre, Sh.60 per acre and Sh.80 per acre respectively. The farmer has Sh.12,600 available for cultivation. Each acre of crop A requires 20 hours of labor, each acre of crop B requires 25 hours of labor and each acre of crop C requires 40 hours of labor. The farmer has a maximum of 5,950 hours of labor available. If he wishes to use all of his cultivable land, the entire budget, and all the labor available how many acres of each crop should be plant? Formulate but do not solve the problem. [3 Marks]
5. The demand and supply functions for a given product are both quadratic functions. Three points for price (p) and quantity (q) have been recorded from the past and are produced below

Price (Shs)	Quantity demanded (Units)	Quantity Supplied (Units)
5	1925	425
10	1700	500
15	1325	625

Required,

1. Derive the demand and supply functions [3 Marks]
2. Determine the equilibrium quantity and equilibrium price. [3 Marks