Linear Programming Part 2

# Linear Programming Part 2 - DS 412 Operations Management...

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DS 412 Operations Management Linear Programming Part II

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Product Mix Example A company produces 4 products A, B, C, and D. Market research shows that no more than 2,000units of A and 1,600 units of C can be sold. Any number of B and D can be sold At least 1000 units of D must be produced to meet a contract agreement. Units of B should not exceed 40% of total production A B C D Available Material #1 3 2 3.5 7 16,000 lbs Material #2 2 3.5 3 0 22,000 lbs Labor 8 5 2 12 40,000 hrs Profit/unit \$80 50 36 50
Product Mix Model Formulation Decision Variables: A, B, C, D where A = number of product A to make B= number of product C to make, and similarly for C and D MAx 80A 50B 36C 50D ST Material 1 3A + 2B + 3.5C + 7D <= 16000 Material 2 2A + 3.5B + 3C <= 22000 Labor 8A + 5B + 2C + 12D <= 40000 Demand A A <= 2000 Demand C C <= 16000 B<=40% -0.4A + 0.6B - 0.4C - 0.4D <= 0 Contract D >= 1000 Non-negativity A, B, C,D >= 0

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Product Mix Excel Formulas 80 50 36 50 Profit =SUMPRODUCT(B3:E3,B2:E2) Constraints: LHS RHS Material #1 3 2 3.5 7 =SUMPRODUCT(\$B\$3:\$E\$3,B7:E7) <= 16000 Material #2 2 3.5 3 0 =SUMPRODUCT(\$B\$3:\$E\$3,B8:E8) <= 22000 Labor 8 5 2 12 =SUMPRODUCT(\$B\$3:\$E\$3,B9:E9) <= 40000 Demand A 1 =SUMPRODUCT(\$B\$3:\$E\$3,B10:E10) <= 2000 Demand C 1 =SUMPRODUCT(\$B\$3:\$E\$3,B11:E11) <= 1600 B <= 40% -0.4 0.6 -0.4 -0.4 =SUMPRODUCT(\$B\$3:\$E\$3,B12:E12) <= 0 Contract D 1 =SUMPRODUCT(\$B\$3:\$E\$3,B13:E13) >= 1000 Changing cells Target Constraint cells
Product Mix: Solver Setup

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Product Mix Optimal Solution 1 2 3 4 5 6 7 8 9 10 11 12 13 A B C D E F G H I 80 50 36 50 Profit 2000 1500 0 1000 285000 Constraints: LHS RHS Material #1 3 2 3.5 7 16000 <= 16000 Material #2 2 3.5 3 0 9250 <= 22000 Labor 8 5 2 12 35500 <= 40000 Demand A 1 2000 <= 2000 Demand C 1 0 <= 1600 B <= 40% -0.4 0.6 -0.4 -0.4 -300 <= 0 Contarct D 1 1000 <= 1000 Which constraints are binding? Which are non-binding?
Product Mix: Sensitivity Report Microsoft Excel 11.0 Sensitivity Report Worksheet: [Book1]Sheet1 Report Created: 10/2/2007 3:27:53 PM Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease \$B\$3 2000 0 80 1E+30 5 \$C\$3 1500 0 50 3.333333333 29.42857143 \$D\$3 0 -51.5 36 51.5 1E+30 \$E\$3 1000 0 50 125 1E+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease \$G\$13 Contarct D LHS 1000 -125 1000 428.5714286 120 \$G\$7 Material #1 LHS 16000 25 16000 1000 3000 \$G\$8 Material #2 LHS 9250 0 22000 1E+30 12750 \$G\$9 Labor LHS 35500 0 40000 1E+30 4500 \$G\$10 Demand A LHS 2000 5 2000 1000 230.7692308 \$G\$11 Demand C LHS 0 0 1600 1E+30 1600 \$G\$12 B <= 40% LHS -300 0 0 1E+30 300 How do we interpret these results?

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Blending Problem A manufacturer of frozen foods produces a food item by mixing four ingredients. The raw materials have the characteristics shown in the table. The manufacturer wants to the food item to have at least 20% protein, at least 25% carbs, and at most 30% fat. What is the best mixture of ingredients that will meet the requirements at a minimum
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## This note was uploaded on 11/10/2011 for the course DS 412 taught by Professor Eng during the Fall '07 term at S.F. State.

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Linear Programming Part 2 - DS 412 Operations Management...

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