SOLUTION: Hi, Would you please be able to help me. I need to understand the formula to add into a graphing tool for the following problem: A minibus operator is contracted to transport 50 O

Algebra ->  Rational-functions -> SOLUTION: Hi, Would you please be able to help me. I need to understand the formula to add into a graphing tool for the following problem: A minibus operator is contracted to transport 50 O      Log On


   

Question 1023712: Hi, Would you please be able to help me. I need to understand the formula to add into a graphing tool for the following problem:
A minibus operator is contracted to transport 50 Olympians from the Olympic Village to the Athletic Stadium. He has three type A minibuses and four type B minibuses available. A type A minibus carries 15 people and a type B minibus carries 10 people. Only five drivers are available. It costs $100 to operate a type A minibus and $80 to operate a type B minibus. He wishes to minimise the costs involved to transport the 50 Olympians.
I've completed the following:
Variables: Let x represent type A mini bus; Let y represent type B mini bus; Let c represent the minimum cost.
Constraints:
x <= 3 (At most 3 type A mini buses available)
y <= 4 (At most 4 type B mini buses available)
x + y = 5 (Limit on number of drivers)
15x + 10y = 50 (Limit on number of passengers who can be carried in both mini buses)
Objective Function: C = 100x + 80y
Graphs - I've set the Axis to x: -1 to 10 and y: -1 to 10 and entered the above relations and constraints but don't know how to enter the formula to determine the minimum cost and I don't understand how corner points work.
Thank you so much for any help you can offer.
Chris
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A minibus operator is contracted to transport 50 Olympians from the Olympic Village to the Athletic Stadium. He has three type A minibuses and four type B minibuses available.
A type A minibus carries 15 people and
A type B minibus carries 10 people.
------
Only five drivers are available.
----------
It costs $100 to operate a type A minibus and $80 to operate a type B minibus.
-------------------------
He wishes to minimise the costs involved to transport the 50 Olympians.
I've completed the following:
Variables: Let a represent type A mini bus; Let b represent type B mini bus;
Let c represent the minimum cost.
Constraints:
a <= 3 (At most 3 type A mini buses available)
b <= 4 (At most 4 type B mini buses available)
a + b <= 5 (Number of drivers)
15a + 10b <= 50 (Limit on number of passengers who can be carried in both mini buses)
Objective Function: C = 100a + 80b
Graphs - I've set the Axis to a: -1 to 3 and b: -1 to 4 and entered the above relations and constraints but don't know how to enter the formula to determine the minimum cost and I don't understand how corner points work.
----
f(a)<= -a + 5
g(a)<= (-3/2)a + 5
----
Draw vertical lines at a = 0 and a = 3
Not
Draw horizontal lines at b = 0 and b = 4
Comment:: That describes the solution area.
Plot f and g in that area.
Find their point of interception.
----
Hope all that helps.
Cheers,
Stan H.
--------------------