The minimum value of C is: 46
The given parameters are:
[tex]C = 6x + 7y[/tex]
Subject to
[tex]x \ge 0[/tex]
[tex]y \ge 0[/tex]
[tex]4x + 3y \ge 24[/tex]
[tex]x + 3y \ge 15[/tex]
To do this, we start by plotting the graphs of the constraints:
The constraints are:
[tex]4x + 3y \ge 24[/tex]
[tex]x + 3y \ge 15[/tex]
See attachment for graph
Next, we identify the corner points.
These are the points where [tex]x \ge 0[/tex] and [tex]y \ge 0[/tex]
From the graph, we have: (0, 8), (3, 4) and (15, 0) as the corner points
Substitute these values in the equation of C
[tex]C = 6x + 7y[/tex]
[tex](x,y) = (0, 8)[/tex] means:
[tex]C = 6 * 0 + 7 * 8 = 56[/tex]
[tex](x,y) = (3,4)[/tex] means
[tex]C = 6 * 3 + 7 * 4 = 46[/tex]
[tex](x,y) = (15,0)[/tex] means
[tex]C = 6 * 15 + 7 * 0 = 90[/tex]
In the above computations, we can conclude that the minimum value of C is: 46
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