1. Solving Linear Optimization Problems Using the Solver Add-in

2. HamburgerFries Fat (g) 10 18 Protein (g) 15 3 Carbohydrate (g) 32 32 Calories (kcal) 220 396 The Diet Problem Julia wonders if she can keep the amount of fat in her diet down and still get all the protein (45 g), carbohydrate (256 g), and calories (1,980 kcal) that she needs every day by eating fast food only. For other nutrients, such as vitamins, iron, and calcium, she will depend on pills (nutritionists would disapprove, but this example ought to be simple). She chooses her favorite fast foods: hamburger and French fries. The nutritive values per serving are given below. How many servings of hamburger and fries would Julia need to eat to satisfy her daily diet requirements? Start with a problem to be formulated

3. constraints that minimizes the total amount of fat subject to the following minimum diet requirements HB = the number of servings of Hamburger FF = the number of servings of French Fries 15 HB + 3 FF >= 45 Protein constraint Julia is looking for objective function 10 HB + 18 FF decision variables nonnegativity constraints 32 HB + 32 FF >= 256 Carbohydrate constraint 220 HB + 396 FF >= 1980 Calories constraint Formulate the Model as a Linear Programming Problem Of course HB >= 0 and FF >= 0

4. Enter labels in cells A2:A6 Preparing the Worksheet for Solver start with blank sheet & enter labels and constants

5. NOTE: The labels in A4:A6 name the 3 constraints in this problem Enter labels in cells B1:E1 Preparing the Worksheet for Solver start with blank sheet & enter labels and constants

6. NOTE: The labels in cells B1:C1 name the 2 variables in this problem Preparing the Worksheet for Solver start with blank sheet & enter labels and constants Enter coefficients of objective function in cells B3:C3 10 HB + 18 FF

7. Preparing the Worksheet for Solver start with blank sheet & enter labels and constants Enter coefficients of left side of Protein constraint in cells B4:C4 15 HB + 3 FF

8. Preparing the Worksheet for Solver start with blank sheet & enter labels and constants Enter coefficients of left side of Carbohydrate constraint in cells B5:C5 32 HB + 32 FF

9. Preparing the Worksheet for Solver start with blank sheet & enter labels and constants Enter coefficients of left side of Calories constraint in cells B6:C6 220 HB + 396 FF

10. Preparing the Worksheet for Solver start with blank sheet & enter labels and constants Enter right sides of constraint in cells E4:E6 15 HB + 3 FF >= 45 32 HB + 32 FF >= 256 220 HB + 396 FF >= 1980

11. Preparing the Worksheet for Solver start with blank sheet & enter labels and constants

12. Highlight the four cells B1:C2 name the cells for the two decision variables Preparing the Worksheet for Solver

13. Starting from the main menu bar click on Insert name the cells for the two decision variables Preparing the Worksheet for Solver

14. Click on Name name the cells for the two decision variables Preparing the Worksheet for Solver

15. name the cells for the two decision variables Click on Create Preparing the Worksheet for Solver

16. Make sure the Top row box is checked name the cells for the two decision variables Preparing the Worksheet for Solver

17. Click OK name the cells for the two decision variables Preparing the Worksheet for Solver

18. Cell B2 has the name HB and is currently blank Cell C2 has the name FF and is currently blank name the cells for the two decision variables Preparing the Worksheet for Solver

19. Click on cell D3 enter the formula for the objective function Preparing the Worksheet for Solver

20. Type = enter the formula for the objective function Preparing the Worksheet for Solver Click on cell B3

21. Type * enter the formula for the objective function Preparing the Worksheet for Solver Click on cell B2

22. enter the formula for the objective function Preparing the Worksheet for Solver Type + Click on cell C3

23. enter the formula for the objective function Preparing the Worksheet for Solver Type * Click on cell C2

24. NOTE: The formula B3*HB+C3*FF could have been typed in cell D3 directly Enter enter the formula for the objective function Preparing the Worksheet for Solver formula entered in D3 objective function (Fat content) 10 HB + 18 FF current value for the formula entered in D3 NOTE: Blanks in HB and FF (cells B2 and C2) are considered zeros

25. Click on cell D3 and grab the fill handle + in the lower right corner copying down the formulas for totals Preparing the Worksheet for Solver

26. Copy the formula in D3 down to cell D6 copying down the formulas for totals Preparing the Worksheet for Solver

27. copying down the formulas for totals Preparing the Worksheet for Solver Click on cell D4 to check your formula formula copied in D4 Protein constraint LHS 15 HB + 3 FF current value for the formula entered in D4

28. copying down the formulas for totals Preparing the Worksheet for Solver Click on cell D5 to check your formula formula copied in D5 Carbohydrate constraint LHS 32 HB + 32 FF current value for the formula entered in D5

29. copying down the formulas for totals Preparing the Worksheet for Solver Click on cell D6 to check your formula formula copied in D6 Calories constraint LHS 220 HB + 396 FF current value for the formula entered in D6

30. Preparing the Worksheet for Solver copying down the formulas for totals NOTE: In the formula, the rows for column B and C have been copied as relative references and the references to the decision variables HB (cell B2) and FF (cell C2), are fixed

31. invoking Solver Add-In from the Tools menu Using Solver Starting from the main menu bar click on Tools

32. invoking Solver Add-In from the Tools menu Using Solver Click on Solver

33. invoking Solver Add-In from the Tools menu Using Solver NOTE: From this point on, only the spreadsheet portion of the Excel window will be displayed

34. select the value of the objective function as the Target Cell Using Solver Click on the Set Target Cell: box

35. select the value of the objective function as the Target Cell Using Solver Click on cell D3 which contains the function we want to optimize

36. indicate if the Target Cell is to be minimized/maximized Using Solver Check the Min radio button to indicate that we want to minimize the value in the Target Cell

37. the Changing Cells are the decision variables Using Solver Click on the By Changing Cells: box

38. the Changing Cells are the decision variables Using Solver Highlight cells B2:C2 containing the decision variables

39. add Constraints Using Solver Click on the Subject to the Constraints: box

40. add Constraints Using Solver Click on Add

41. select the constraints’ left-hand-sides Using Solver Click on the Cell Reference: box

42. select the constraints’ left-hand-sides Using Solver Highlight cells D4:D6

43. select the constraints’ left-hand-sides Using Solver

44. select the constraints’ types Using Solver Click on 

45. select the constraints’ types Using Solver Click on >=

46. Click on the Constraint: box select the constraints’ right-hand-sides Using Solver

47. Highlight cells E4:E6 select the constraints’ right-hand-sides Using Solver

48. NOTE: Since the three constraints in the Diet Problem are of type >= they can be added all at once. Click on OK select the constraints’ right-hand-sides Using Solver

49. setting the Options Using Solver Click on Options

50. setting the Options Using Solver Check Assume Linear Model and Assume Non-Negative boxes (do not modify the other Options for this problem)

51. setting the Options Using Solver Click OK

52. executing Solver Using Solver Click on Solve

53. obtaining solutions from the worksheet Using Solver Solver uses a method known as SIMPLEX This solution contains Protein: 105 g Carbohydrate: 256 g Calories: 1980 kcal satisfying the constraints Solver finds a solution HB = 6.75 servings of Hamburger FF = 1.25 servings of French fries with minimum fat content of 90 g

54. obtaining an Answer Report Using Solver Click on Answer in the Reports box

55. obtaining an Answer Report Using Solver Click on OK

56. Click on Answer Report 1 tab viewing the Answer Report Using Solver

57. NOTE: From this point on, only the spreadsheet portion of the Excel window will be displayed viewing the Answer Report Using Solver

58. viewing the Answer Report Using Solver Final steps in any solution involve an interpretation of these computer-generated results with minimum fat content of 90 g Solution HB = 6.75 servings of Hamburger FF = 1.25 servings of French fries and with Protein: 105 g Carbohydrate: 256 g Calories: 1980 kcal satisfying the constraints