Formulate the problem as a linear programming model and solv

Formulate the problem as a linear programming model and solve using the computer. The interstate Truck Rental firm has accumulated extra trucks at three of its truck leasing outlets, shown in the following table.

Solution

Objective function :

Minimize Z = 70x₁₁ + 80x₁₂+45x₁₃+90x₁₄+120x₂₁+40x₂₂+30x₂₃+75x₂₄+110x₃₁+60x₃₂+70x₃₃+80x_34.

Subject toconstraint,

x₁₁+x₁₂+x₁₃+x₁₄ = 70 ; x₂₁+x₂₂+x₂₃+x₂₄ = 115 ; x₃₁+x₃₂+x₃₃+x₃₄ = 60 . (Supply Constraint)

x₁₁+x₂₁+x₃₁=80 ; x₁₂+x₂₂+x₃₂=50 ; x₁₃+x₂₃+x₃₃=90 ; x₁₄+x₂₄+x₃₄ =25 . (Demand Constraint)

	A	B	C	D	Supply
1	70	80	45	90	70
2	120	40	30	75	115
3	110	60	70	80	60
Demand	80	50	90	25	245