Let x package nuts and y package bolts are produced
Let z be the profit function, which we have to maximize.
Here z = 17.50x + 7y ... (i) is objective function.
And constraints are
x + 3y ≤12 ...(ii)
3x + y ≤12 ...(iii)
x≥ 0 ...(iv)
y≥0 ...(v)
On plotting graph of above constraints or inequalities (ii), (iii), (iv) and (v) we get shaded region as feasible region having corner points A, O, B and C.
For coordinate of ‘C’ two equations
x + 3y = 12 ...(vi)
3x + y = 12 ...(vii) are solved
Applying (vi) × 3 – (vii), we get
3x + 9y - 3x - y = 36 - 12
=> 8y = 24 => y = 3 and x = 3
Hence coordinate of C are (3, 3).
Now the value of z is evaluated at corner point as
Therefore maximum profit is Rs.73.5 when 3 package nuts and 3 package bolt are produced.