Chrissy is a health and fitness coach. She wants to create a nutritional supplement, which meets the required daily dose of key nutrients at the lowest cost. Her goal is to sell this blend to her own clients to ensure that their nutritional needs are met in the most efficient manner possible. She decides to combine three different protein powders in order to create her own blend. The price of Type A Protein Powder is $25 per pound and it contains 42 gms of protein, 12 gms of carbohydrates and 4 gms of fat per serving. The price of Type B Protein Powder is $10 per pound and it contains 20 gms of protein, 20 gms of carbohydrates and 2 gms of fat per serving. The price of Type C Protein Powder is $8 per pound and it contains 10 gms of protein, 5 gms of carbohydrates and 10 gms of fat per serving.Each pound of any protein powder is equivalent to 12 servings. Chrissy runs a cost minimization linear program and identifies the blend would result in the lowest cost of $15.94 per pound of her own mix in order to meet the minimum requirements of 60 gms of protein, 45 gms of carbohydrates, and 20 gms of fat per serving. Her sensitivity report is given here.

Based on the report, answer the following questions: Write out the Linear Program (equations) that Chrissy might have used. What is the optimal solution that Chrissy obtained? Total Minimum Cost? Specify the objective function ranges. What do they mean? (in words) Identify each of the Right-Hand Side ranges. What do they mean? (in words) Interpret the shadow prices of each constraint (in words).

Microsoft Excel 16.0 Sensitivity Report Worksheet: [Final Solutions.xlsx]Sheet1 Variable Cells Final Reduced Cell Name Value Cost $B$9 A 1.066 0 $C$9B 1.148 $D$9 C 0.3600 Objective Coefficient 25 10 8 Allowable Increase 5.80 11.94 6 .44 Allowable Decrease 11.32 1.53 5.60 Constraints Cell Name $C$14 Protein LHS $C$15 Carbs LHS $C$16 Fat LHS Final Value 720 540 240 Shadow Price 0.0331 0.0089 0.0517 Constraint Allowable R.H. Side Increase 720 2 34.00 540 260.00 240 1238.57 Allowable Decrease 365.05 196.42 39.00 Microsoft Excel 16.0 Sensitivity Report Worksheet: [Final Solutions.xlsx]Sheet1 Variable Cells Final Reduced Cell Name Value Cost $B$9 A 1.066 0 $C$9B 1.148 $D$9 C 0.3600 Objective Coefficient 25 10 8 Allowable Increase 5.80 11.94 6 .44 Allowable Decrease 11.32 1.53 5.60 Constraints Cell Name $C$14 Protein LHS $C$15 Carbs LHS $C$16 Fat LHS Final Value 720 540 240 Shadow Price 0.0331 0.0089 0.0517 Constraint Allowable R.H. Side Increase 720 2 34.00 540 260.00 240 1238.57 Allowable Decrease 365.05 196.42 39.00