9. The description of a linear programming model for a minimum-cost-per-day balanced diet and the EXCEL answer and sensitivity reports are reproduced on the two sheets distributed with this exam. Use this information to answer the following questions. How many ounces of each food are in the minimum cost diet? CEREAL MILK (2) b. What will be the daily cost of this diet? F With rising grain prices, there are concerns that the cost for CEREAL could rise as high as 3.5 cents. If this happens, will the minimum cost diet change? Identify the information you used to answer this question. (4) d. It may be possible to purchase 5 milligram iron supplement pills that could be distributed along with the CEREAL and MILK diet. If the cost of each 5- milligram pill is 10 cents, would you recommend adding one pill to the daily diet for each person? Identify the information you used to answer this question. (4) How much would the minimum cost of the daily diet increase if the vitamin D requirement was increased from 400 LU. to 500 IU? Identify the information you used to answer this question. Linear programming Problem for Question 9 A nutritionist working for a United Nations food distribution agency has been asked to develop a minimum-cost-per-day balanced diet comprised of just two foods: cereal and dried milk. Each ounce of cereal costs 3 cents and provides 2 grams of protein, 100 calories of energy, 10 I.U. of Vitamin D, and 1 milligram of iron. Each ounce of dried milk costs 2 cents and provides 5 grams of protein, 40 calories of energy, 15 1.U. of Vitamin D, and 0.5 milligrams of iron. The minimum daily requirements are 100 grams of protein, 500 calories, 400 1.U. of vitamin D, and 20 milligrams of iron. I have formulated a linear programming model to identify the mix of cereal and dried milk that will minimize the daily cost of the diet while meeting all the nutritional requirements. The tableau for this model is presented below, and the Excel output is on the following page. CEREAL MILK min 3 2 S.I 2 5 100 40 10 15 1 0.5 Y Y Y Y All activities >0 Cost 100 Protein 500 Energy 400 Vit D 20 Iron Answer Report Objective Cell (Min) Cell Name $G$2 Cost Original Value Final Value 70 Variable Cells Cell Name Original Value Final Value Integer $B$9 CEREAL 0 10 Contin SC$9 MILK 0 20 Contin Constraints Cell Name Cell Value Formula Status Slack $G$4 Protein Not 120 $G$4-SES4 Binding 20 Not $G$5 Energy $G$6 Vit D $G$7 Iron 1800 SGSS-SESS Binding 400 SGS6 SES6 Binding 20 SGS7>-SE$7 Binding 1300 0 Sensitivity Report Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase $B$9 CEREAL 10 0 3 Decrease 1 1.666666667 $C$9 MILK 20 0 2 2.5 0.5 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $G$4 Protein 120 0 100 20 1E+30 $G$5 Energy 1800 0 500 1300 1E+30 $G$6 Vit D 400 0.05 400 200 50 $G$7 Iron 20 2.5 20 10 6.666666667