. MANUFACTURING PROFIT A manufacturer estimates that cach unit of a particular commodity can be sold for $3 more than it costs to produce. There is also a fixed cost of $17,000 associated with the production of the commodity. a. Express total profit P(x) as a function of the level of production x. b. How much profit (or loss) is there when x = 20,000 units arc produced? When 5.000 units are produced? (a) Find the value of x. for which equilibrium occurs and the corresponding equilibrium price p.. (b) Sketch the graphs of the supply and demand curves, p = S(x) and p = D(x). on the same graph. (c) For what values of x is there a market shortage? A market surplus? S(x) = 3x + 150 and D(x) = 2x + 275 S(x) = 2x + 7.43 and D(x) = 0.21x 0.84x + 50 Practice sheet 1 1. Determine the domain of the given functions x+7 Jf('c):}r2+2x8 x="7 k(x) = x2 -9 g(x) =v18 3x 3 1) = = h(x) =x 2x%2+7 2. Find the equation of the line passes through (2,1) and (-1, 4). Graph the line. a. Find the x and y intercept of the following function y=x*-2x+2 Quadratic formula: A=b? 4ac and Xy, = 1&-\\% b. Find all points of intersection (X, y) of the graphs f(x)=2x+2and g(x) =-x*2x+2 c. Sketch the graphs of the functions and show the intersection points on the graph. (Hint: to graph g(x) use information from number 3) . A manufacturer can sell a certain product for $20 per unit. Total cost consists of a fixed overhead of $1000 plus production costs of $7 per unit. (0.5+0.5+1=2 points) a. Find the revenue function in terms of the level of production x b. Find the profit function in terms of the level of production x . For which level of production will revenue equals cost? What do we call this point in business terms? i 7. SUPPLY AND DEMAND When electric blenders are sold for p dollars apiece, manufac turers will supply blenders to local retailers. while the local demand will be 60 - p blenders. At what market price will the manufacturers' supply of electric blenders be equal to the consumers' demand for the blenders? How many blenders will be sold at this price? 8. BREAK-EVEN ANALYSIS A furniture manufacturer can sell dining room tables for $500 apiece. The manufacturer's total cost consists of a fixed overhead of $30,000 plus production costs of $350 per table. a. How many tables must the manufacturer sell to break even? b. How many tables must the manufacturer sell to make a profit of $6,000? c. What will be the manufacturer's profit or loss if 150 tables are sold? d. On the same set of axes, graph the manufac turer's total revenue and total cost functions. Explain how the overhead can be read from the graph