100 printers of Type A
Let x be the no. of printers of type A
Let y be the no. of printers of type B
You expect to sell at least 100 laser printers this month
Equation becomes : —1
Cost of 1 printer of Type A = $86
Cost of x printer of Type A = $86x
Cost of 1 printer of type B =$135
Cost of y printer of type B =$135 y
Minimize cost function:
Now Profit on 1 Type A printer = $45
Profit on x Type A printer = $45x
Profit on 1 Type B printer = $35
Profit on y Type B printer = $35y
We are given that you need to make at least $3850 profit on them.
So, equation becomes : —2
Conditions : —3 and —4
Now plotting the lines 1,2,3,4 on the graph
Refer the attached figure
Feasible points are (100,0);(0,100)and(35,65)
Now check which feasible point provides minimum cost.
At point (100,0)
So, At point (100,0) total cost is $8600.
At point (0,100)
So, At point (0,100) total cost is $13000
At point (35,65)
So, At point (35,65) total cost is $11460
So, at (100,0) we are getting the minimum cost i.e. $8600.
So, we need to order 100 printers of type A and 0 printers of type B to minimize the cost.