Assume that you graph a system of constraints and find vertices (0,8), (9,4), (8,5), and (8,0).

Question

Evaluate the objective function at each vertex to find the minimum value: P = 100y - 20x - 12. For your answer, type the point at which the minimum occurs. Do NOT type the value.

Answer 1

The given vertices are points that are to be evaluated your

objective function "P".  Evaluate them as follows...

 

P=100y-20x-12..........objective function, given, problem statement

 

Point (0,8):

P₁=100(8)-20(0)-12...substitute "x and y"

   =800-0-12...............simplify

   =788

 

Point (9,4):

P₂=100(4)-20(9)-12

   =400-180-12

   =208

 

Point (8,5):

P₃=100(5)-20(8)-12

   =500-160-12

   =328

 

Point (8,0):

P₄=100(0)-20(8)-12

   =0-160-12

   =-172...................minimum value for objective function "P"

 

So the vertex with coordinates (8,0) produces the

minimum value for the objective function "P".

 

Answer 2

There are four vertices.  Apparently, they have names.  For example, A (0,8), B (9,4), C(8,5) and D (8,0) or are referred to using just their (x,y) coordinates.

 

The objective function calculates some value that depends on (x,y) and is either maximized or minimized at one or more of these four points.  This problem asks where the minimum value of the objective function occurs.  So, you must calculate the objective function for each of these four number pairs and then select the number pair (not the objective function value) where the objective function has the smallest value.