Monday, December 6, 2010

Ch 3.4 Linear Programming

For this chapter 4 linear programming project, we have to came up with a problem and graph it. My problem was : I went to the store to purchase books for the 14 days Christmas break. I could finish an English book in 2 days and a Chinese book in 5 days. The store is doing a holiday discount, every English book cost \$2.50 and every Chinese book cost \$4. The most I plan to spend on books are \$24. C represents the number of Chinese books, e is the numbers of English books. The constraints are :
1) c is greater than or equal to 0
2) e is greater than or equal to 0
3) 5c+2e is less than or equal to 14
4) 4c+5e is less than or equal to 24
On the image above I have graph each constraints separately. I shade the first constraint with pink, the second constraint with yellow. To graph the third one I plot the intercepts and connect it with a solid line, than I shade below that line with blue. For the last constraints I used the same process but this time I shade below it with red. When I overlap the 4 constraints together I get the final result. The part where all colors overlap is the feasible region, which is shaded brown above. By looking at the final result you can see that the vertices are : (0,0) , (2.8,0) , (0,4.8) , and (1.3,3.9)