2. Linear Programming ... 1
• A method of allocating resources in an
optimum way
• A decision making tool for all industries
• A mathematical method to maximize profits of
minimize costs
• Resources are decision variables
• Objective function = criteria for selecting the
best values for these variables
3. Linear Programming ... 2
• Limitations on resource availability are called
constraints set
• Linear = the criteria for selecting the variables
can be linear
• Entire problem can be expresses as straight
lines of planes
• Non-negativity constraints
4. Linear Programming Formula
• Maximize Z = C1*X1 + C2*X2 + .... +Cn*Xn
• Subject to
– A11*X1 + A12*X2 + .... + A1n*Xn < = B1
– A21*X1 + A22*X2 + .... + A2n*Xn < = B2
– ---– ---– Am1*X1 + Am2*X2 + .... +Amn*Xn <= Bm
• C, Amn and Bm re given constraints
5. Linear Programming Example
• A company making Hockey Sticks and Chess sets
• Hockey stick profit = $2, Chess set = $4
• Hockey stick takes 4 hours and Machine A and 2
hours at Machine B
• Chess takes 6 hours at Machine A and 6 hours at
Machine B and 1 hour at Machine C
• Machine A has max 120 hours capacity per day,
Machine B has 72 hours and machine C has 10
hours
6. Formulation
• H = number of Hockey sticks and C = number
of chess sets
• Maximize Z = $2*H + $4*C
• 4*H + 6*C <= 120 (Machine A)
• 2*H + 6*C <= 72 (Machine B)
• 1*C <= 10 (Machine C)
• H , C >= 0
7. Transportation
• Special case of Linear Programming
• Maximize profits, minimize costs of shipping
• N units, M destinations