Question

Q18 Optimization problem 14 Points OSU wants to rent several vehicles to transport at least 750 students to a company tour in Portland. A bus costs $800 to rent and can transport 50 people whereas a van costs $300 to rent and can carry up to 15 people. The company offers to waive the driver fee if the university rents at least 10 vans. Find the optimal number of buses and vans that will minimize costs. Q18.1 Question 2 Points Write down the question of interest. Enter your answer here

these are all part of one question.

Answer 1

0.18.1 and Here the number of required buses vans must be positive integers that minimizes total cost. We use. Graphical method to solve the problem. x= the number of buses y = the number of vans objective function Minimize c(x, y) 800x + 30oy Q18.2 Q18.3 Q18.4 The constraints are 50% +157 2750 y zlo a zo a and y are integers. 1 218.5 The graph is w (0,50 )A YZIO B (12, 10) u >ge - 50xtiny 2 750

We get the unbounded feasible region with two extreme points (critical points) A (0,50) B (12,10). avel Now we calculate the cost function com at two critical points. these CA 8oox ot 300x50 15000 CB = 800 x 12 + 300x10 =(12600 the minimum cost occurs at B (12,10). so, the optimal solution is x=12, y=10, cu 12600 min Q18.6 so, the required number of buses = (12 required number of vans=0 Also minimum cost is is = $ 12600