set up dont solve

Question

set up dont solve. the texas technical institute for turtle tutelage offers classes in language, mathematics, and physics. language courses are worth 3 credit , math courses worth 4 credit , and physics are worth 5 credit. the prise to take a language course is $15, math course is $12, physics course is $18. to graduate, sydney the turtle must take at least 35 classes and accumulate a minimum of 130 credits. in addition, the college requires that a minimum of 5 each type of course be taken. how many courses of each type should sydney take if she wants to minimize the cost of her education?

Answer 1

As you stated, this is a linear programming problem. 

 

First let's choose the variables...  Let x = the number of language courses, let y = the number of math courses, and let z = the number of physics courses.

 

The objective function to be minimized is the total cost.  Based on the prices given, that's 15x + 12y + 18z.

 

Now let's use the other information to create the constraints.

 

"sydney the turtle must take at least 35 classes"

x + y + z ≥ 35

 

"and accumulate a minimum of 130 credits"

3x + 4y + 5z ≥ 130

 

"a minimum of 5 each type of course be taken"

x ≥ 5

y ≥ 5

z ≥ 5

 

So to summarize...

 

The objective function is 15x + 12y + 18z, and it is to be minimized.

 

There are 5 constraints:

 

x + y + z ≥ 35

3x + 4y + 5z ≥ 130

x ≥ 5

y ≥ 5

z ≥ 5