Solve the following LP Maximize $4x + $5y Subject to            4x + 5y ≤ 72                                 6x + 5y ≥ 27                                 -3x + 8y ≥ 0                                 x, y ≥ 0 a) Write the original optimal solution and objective function value. b) What is the optimal solution and objective function value if the profit per unit of x decreases to $1? c) What is the optimal solution and objective function value if the first constraint changes to 4x + 5y ≤ 80 d) What is the optimal solution and objective function value if the third constraint changes to -3x + 8y ≤ 0?

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