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 




Solution (vertex points) 

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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