Linear Programming 1.6 (M3) p. 30 Test Friday !!
Vocabulary Linear programming: maximizing/minimizing a linear objective function. Objective function: gives quantity that is to maximized or minimized and subject to constraints Constraints: boundaries of a function Feasible region: solution area shaded when all constraints are graphed –If bounded (definite shape) then it has a max./min. –The max./min are the vertices.—This is what you substitute into your objective function.
Find the minimum value and the maximum value of the objective function C= 2x + 8y subject to the following constraints.
Min.: 0, Max.: 56
Use Linear Programming to maximize profit Wagons are sold at a craft fair. It takes 4 hours to make a small one and 6 hours to make a large one. The owner will make a profit of $12 for a small wagon and $20 for a large one. He has no more than 60 hours available to make the wagons and wants to have at least 6 small wagons to sell. How many of each size should be made to maximize the profit? Let x = # of small wagons; y = # of large Write the equation for profit: Constraints: –small wagon –Large wagon –Number of hours:
Use Linear Programming to maximize profit Let x = # of small wagons; y = # of large Write the equation for profit: P = 12x + 20y Constraints: –small wagon: –Large wagon –Number of hours: Objective Function P = 12x + 20y
A storeowner wants to limit the weekly payroll to $960. Employees working regular hours receive $4 per hour, and employees working overtime receive $6 per hour. On the average the store makes $18 for each regular hour of employee work and $32 on each over time hour of employee work. If overtime hours are restricted to at most 2/3 of the regular hours, how should the owner schedule working hours to maximize profit? Objective Function: P = 18x + 32y Constraints: Additional Practice – back side of worksheet #2
Objective Function: P = 18x + 32y Constraints:
Additional Practice – back side of worksheet #1 x = $ in 6% y = $ in 12% Objective Function: P =.06x +.12y Constraints: