Linear Programming CCC Co. sells three products, 1, 2, and 3 with demand of 700 units, 100 units and 500 units respectively. There is a contractual obligation to make at least 10 units of each product. Each of the products utilize different numbers of hours in each of two unique departments, mixing and baking. The specific use of the departmental hours by each of the products is as follows: Department Baking hours used per unit Mixing hours used per unit Product Usage (in hours) 1 2 3 1.4 2.9 3.3 0.9 3.1 2.1 Sensitivity Report Variable Cells Cell Name $B$8 A $B$9B $B$10 C Final Value 700 10 451.8181818 Reduced Cost 0.060606 -1.30303 0 Objective Coefficient 6 11 14 Allowable Allowable Increase Decrease 1E+30 0.060606061 1.30303 1E+30 0.14285 1.482758621 Constraints Cell $E$2 $E$3 Name Baking used Mixing used Final Shadow Value Price 2500 4.242424242 1609.818182 0 Constraint R.H. Side 2500 3900 Allowable Increase 159 1E+30 Allowable Decrease 1458 2290.181818 a) State all production constraints (input and output) in the form of mathematical inequalities b) State which product would be produced if an extra baking hour could be obtained, and why it is the choice. c) Prove the shadow price of the baking constraint by showing how it is calculated. Linear Programming CCC Co. sells three products, 1, 2, and 3 with demand of 700 units, 100 units and 500 units respectively. There is a contractual obligation to make at least 10 units of each product. Each of the products utilize different numbers of hours in each of two unique departments, mixing and baking. The specific use of the departmental hours by each of the products is as follows: Department Baking hours used per unit Mixing hours used per unit Product Usage (in hours) 1 2 3 1.4 2.9 3.3 0.9 3.1 2.1 Sensitivity Report Variable Cells Cell Name $B$8 A $B$9B $B$10 C Final Value 700 10 451.8181818 Reduced Cost 0.060606 -1.30303 0 Objective Coefficient 6 11 14 Allowable Allowable Increase Decrease 1E+30 0.060606061 1.30303 1E+30 0.14285 1.482758621 Constraints Cell $E$2 $E$3 Name Baking used Mixing used Final Shadow Value Price 2500 4.242424242 1609.818182 0 Constraint R.H. Side 2500 3900 Allowable Increase 159 1E+30 Allowable Decrease 1458 2290.181818 a) State all production constraints (input and output) in the form of mathematical inequalities b) State which product would be produced if an extra baking hour could be obtained, and why it is the choice. c) Prove the shadow price of the baking constraint by showing how it is calculated