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| PAGE: 784 | SET: Exercises | PROBLEM: 29 |
Let 
be the number of the metal fastener.
Let 
be the number of the plastic fastener.
Cost of each metal fastener is 
.
Cost of each metal fastener is 
.
Total cost of six samples is 
.
Hence the constraint is 
.
Entrepreneur wants to produce at least two of each samples.
Hence the constraints are 
.
It takes 
hours to produce metal fastener and 
hours to produce plastic fastener
It does not exceed 
hours.
Hence the constraint is 
.
The objective function is .
The constraints are
Graph :
Graph the inequalities and shade the required region.
Note : The shaded region is the set of solution points for the objective function.
Observe the graph:
Tabulate the solutions of each of two system of inequalities and obtain the intersection points.
|
System of boundary equations |
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| Solution (vertex points) |  |
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Find the value of objective function at the solution points.
At point 
, 
.
At point 
, 
.
At point 
, 
.
At point 
, 
.
Observe the values of 
:
The minimum value of 
is
at .
Therefore, entrepreneur should make 
metal fastener and 
plastic fastener for total cost of
.
Entrepreneur should make metal fastener and plastic fastener for total cost of 
.
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