Matematika | Analízis » Christmas Tree Problem, Linear Programming

Name Linear ProgramminG Date Period Christmas tree Problem Monica Pety runs a gift shop in which she sells expensive trees at Christmas time. Her supplier, Connie Furr, charges her $80 for each real tree, and $160 for each artificial tree. Monica is hard-up for cash this year, and wants to invest the minimum amount in trees. a) Define variables for the number of real and artificial trees you can buy. b) Write an objective quantity expressing the total investment in terms of your two variables. c) Write inequalities expressing each of the following requirements: i) Monica can buy between 20 and 90 real trees, inclusive. ii) She can buy up to 100 artificial trees. iii) Connie can supply anywhere between 50 and 120 trees, total. iv) Connie requires that the number of artificial trees ordered be at least half the number of real trees. d) Use this space to find and list your corner points: e) Plot the graph of the system in part

c. Label the vertices f) Find the minimum value of the objective quantity. How many of each kind of tree should Monica buy? What is her minimum investment?