1. Optimization using LP models Repco Pharmaceuticals (Ex 4.6) Ravi Krishna Ravula Dsc 8240

2. Situation and Objective  Repco is a Drug Mfg company  It produces 3 drugs (A,B,C) and are sold @ $8, $70 and $100 respectively.  2 units of A are required to produceB  1 unit of B is required to produce C  Objective: Maximize sales revenue

3. Variables and Measures Input Variables: Required labor hrs to produce a unit Unit of a product used to produce another product Unit selling price of each drug. Output variables: Revenue from Sales. Amount of products sold Constraints: Amount produced = Amount used to produce other products + Amount sold Total labor hours available Goods used in producing another product cannot be sold. Decision Variables: Amount of goods produced (these are the trial values)

4. Mathematical formulation Labor hrs reqd to produce A = 1 hr. B = 2 + 2 = 4 hrs and C = 3 + 4 = 7hrs Unit of product used to produce another product. A B C A B C A 0 2 0 A 0 2 0 B 0 0 1 B 0 0 1 C 0 0 0 C 0 0 0 Amount of products sold = Units produced – Units used as inputs to produce other units Revenue from Sales = Sum of each Product unit selling price * amt of product sold

5. Spreadsheet model  The inputs are in the green box on the left side.  The grey shaded area has the ranges  The production plan is in orange colored cells.  The production plan includes the changing cells (units produced) and output cells (units sold)  The yellow cells show the Balance constraints  The red and blue cells show the Revenue (Target cell)

6. Using Solver After invoking the solver, and filling in the target cell (Revenue), changing cells (Units produced, sold) and the constraints, click on options and choose Non-negativity and linear model assumption.

7. Optimum Solution from Solver  Optimal Production A = 20 units, B =10 units.  Optimal revenue is $700  All units of A are used to produce B  Only product B is being sold.  Though C has the highest selling price it is not being formed because it involves larger labor requirements. (View in excel) View in excelView in excel

8. Sensitivity Analysis  To see how the optimal solution changes as we change one or more of the inputs  Solver table is invoked to perform sensitivity analysis.

9. One way table  Sensitivity of revenue, units produced and units used as inputs to product C selling price.  with the price of C at $130, there is a production of 5.714 units of C, resulting in revenue of $743.  Only product C is being sold.

10. Using a 2-way table  Sensitivity of amount of C produced to selling price of C and labor hour availability  Though there is an increase in labor hours there is no production in C till the price reaches $130

11.  It was seen that though there is an increase in labor hours there is no production in C till the price reaches $130 as it was in the previous analysis.  B requires 4 labor hours and C needs 7 hours. Revenue of B for one unit is $70. when divided by Labor hours needed it shows that $17.50 is revenue per labor hour.  To earn more C should sell at a minimum of 7 * 17.50 = $122.50.