a. Find the break-even point for the firm. b. If the company produces and sells 2000 units, would they obtain a profit or loss? c. If the company produces and sells 3000 units, would they obtain a profit or loss?

Math 1313 Section 1.5 5Example 7:Given the following profit function P(x) = 6x -12,000. a. How many units should be produced in order to realize a profit of $9,000? b. What is the profit or loss if 1,000 units are produced? Example 8:A bicycle manufacturer experiences fixed monthly costs of $124,992 and variable costs of $52 per standard model bicycle produced. The bicycles sell for $100 each. How many bicycles must he produce and sell each month to break even? What is his total revenue at the point where he breaks even?

Math 1313 Section 2.1 1Section 2.1: Solving Linear Programming ProblemsDefinitions:Anobjective functionis subject to a system of constraints to be optimized (maximized orminimized)Constraintsare a system of equalities or inequalities to which an objective function is subjectto.Alinear programming problemconsists of an objective function subject to a system ofconstraintsExample of what they look like:Anobjective functionis max P(x,y) = 3x + 2y or min C(x,y) = 4x + 8yConstraintsare a :60y6x2120y3x5Alinear programming problemconsists of a both the objective function subject torestraints.MaxyxyxP23ሻ,ሺSt:0y,x80y5x24yxConsider the following figure which is associated with a system of linear inequalities:Definitions:The region is called afeasible set. Each point in the region is a candidate for the solution ofthe problem and is called a feasiblesolution.The point(s) in region that optimizes (maximizes or minimizes) the objective function is calledtheoptimal solution.Fundamental Theorem of Linear ProgrammingGiven that an optimal solution to a linear programming problem exists, it must occur ata vertex of the feasible set.