Problem 3: Sensitivity Analysis Exercise - Model Instructions: This is the model for the problem attached on the right side. The sensitivity report for this model is on the next worksheet. Based on this model and the sensitivity report, answer the questions on worksheet "Problem 3-Questions". Aluminum Mill 1 Mill 2 High 6 2 Medium 2 2 Low 4 10 Cost per day 6000 7000 Operation days Mill 1 Mill 2 4 0 Total cost 24000 Production Quantity 24 8 16 Demand 12 United Aluminum Company of Cincinnati produces three grades (high, medium. and low) of aluminum at two mills. Each mill has a different production capacity (in tons per day) for each grade, as follows: Mill Aluminum Grade 1 2 High 6 2 Medium 2 2 Low 4 [0 The company has contracted with a manufacturing rm to supply at least 12 tons of high-grade aluminum. 8 tons of medium-grade aluminum. and 5 tons of low-grade aluminum. It costs United $6.000 per day to operate mill 1 and $7,000 per day to operate mill 2. The company wants to know the number of days to operate each mill in order to meet the contract at the minimum cost. Problem 3: Sensitivity Analysis Exercise - Sensitivity Report Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$15 Mill 1 4 0 6000 1000 6000 $C$15 Mill 2 O 1000 7000 1E+30 1000 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$7 High Production Quantity 24 0 12 12 1E+30 $D$8 Medium Production Quantity 8 3000 8 1E+30 4 $D$9 Low Production Quantity 16 0 5 11 1E+30Problem 3: Sensitivity questions 1. What is the current optimal solution and the objective function value? 2. What is the objective function coefficient of decision variable 1 (operation days of mill 1)? 3. What is the sensitivity range for the objective function coefficient of decision variable 1 (operation days of mill 1)? 4. If the operation cost of mill 1 increases from $6000 to $7500, will the optimal solution change? And why? 5. What is the objective function coefficient of decision variable 2 (operation days of mill 2)? 6. What is the sensitivity range for the objective function coefficient of decision variable 2 (operation days of mill 2)? 7. If the operation cost of mill 2 decreases from $7000 to $6500, will the optimal solution change? And why? 8. Which constrains are binding? 9. If we can decrease the demand of highgrade aluminum by 2 tons at the cost of SlOOO/ton, is it worth doing this? And why? 10. If the demand of medium-grade aluminum increases by 4 tons, what is the new total cost? And why? 11. If we can purchase 2 tons of mediumgrade aluminum from our competitors at SZOOO/ton to satisfy part of the demand, instead of making it in our mills (in other words, we can decrease the demand by 2 tons at the price of SZOOO/ton), is it worth doing this? And why? 12. If the customer needs additional 5 tons of lowgrade aluminum and is willing to pay $1000/ton, do we want to accept this offer? And why? 13. If the customer needs additional 20 tons of lowgrade aluminum and is willing to pay $1000/ton, do we want to accept this offer? And why