An entrepreneur is having a design group produce at least nine samples of a new kind of fastener that he wants to market. It costs $3.00 to produce each metal fastener and $9.00 to produce each plastic fastener. He wants to have at least two of each version of the fastener and needs to have all the samples 42 hours from now. It takes 5 hours to produce each metal sample and 1 hour to produce each plastic sample. To minimize the cost of the samples, how many of each kind should the entrepreneur order? What will be the cost of the samples?
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Mathematical model of proble is
Let C be the cost. P be the no. of the plastic fastener and M be the no of metal fastener.
At least constraints.
So Problem is
Now draw the graph M- along x-axis and P along y-axis
The solution of set of inequality is
P(2,32) ,Q(8,2) and R(2,2)
In graph Q is point of intersection of red and green line.
P is point of intersection of redline and x=2.
R is point of intersection of lines x=2 and y=2
C at P=3x2+9x32
C at Q=3 x 8+9 x2
C at R= 3x2+9x2
Thus Min( 294,42,24)=24
Min cost is=$24 at R(2,2)
P=2 ad M=2
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