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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