1.) Cost Revenue Model: Roberto operates a delivery service in a large city. His start up cost amounted to $3900. He estimates that it costs him (in terms of gasoline, wear and tear on his car, etc.) $4 per delivery. He charges $7 per delivery. Let X represent the number of deliveries he makes.
A.) Express the cost C as a function of x, C(x)
B.) Express the revenue R as a function of x, R(x).
C.) Determine the value for which revenue equals cost, R(x)=C(x).
D.) Graph y=C(x) and y=R(x) on the same axes. Answer the question.
2.) Region Of Feasible Solution: You are given the constraints and the objective function. Find where f(x,y)= 6x-7y+42 is maximized and minimized. Indicate both the point and the Maximum/minimum value at that point. Use graphical methods to solve.
A.) 4y-7yB.)y+2xC.)7y-x /> -18
3.) Linear Programing Problem: Seall Manufacturing Company makes television monitors. It produces a bargain monitor that sells for $100 profit and a deluxe monitor that sells $150 profit. On the assembly line the bargain monitor requires 3 hr., while the delux monitor takes 5 hr. The cabinet shop spends 1 hr. on the cabinet for the bargain monitor and 3 hr. on the cabinet for the delux monitor. both models require 2 hr. of time for testing and packing. On a particular production run, the Seall Company has available 3900 work hours on the assembly line, 2100 work hours in the cabinet shop, and 2200 work hours in the hours on the assebly line, 2100 work hours in the cabinet shop, and 2200 work hours in the testing and packing department. How many of each model should it produce to make the maximum profit? What is the maximum profit?
A.) Assign Variables
B.) Write down the constraints and objective function.
C.) Graph the constraints, find the region of feasible solutions, and lable the vertices
D.) Find the value of the objective function at each vertex.
E.) Answer the question.