You can use a calculator to do numerical calculations. No graphing calculator is allowed. Please DO NOT USE ANY COMPUTER SOFTWARE to solve the problems.(b) What is a diet problem? Briefly discuss the objective function and constraint requirements in a diet problem. Give a real world example of a diet problem.(c) What are the differences between QM for Windows and Excel when solving a linear programming problem? Which one you like better? Why?(d) What are the dual prices? In what range are they valid? Why are they useful in making recommendations to the decision maker? Give a real world example.Let P1 = number of Product 1 to be producedP2 = number of Product 2 to be producedP3 = number of Product 3 to be producedP4 = number of Product 4 to be producedMaximize 80P1 + 100P2 + 120P3 + 70P4 Total profitSubject to10P1 + 12P2 + 10P3 + 8P4 3200 Production budget constraint4P1 + 3P2 + 2P3 + 3P4 1000 Labor hours constraint5P1 + 4P2 + 3P3 + 3P4 1200 Material constraintP1 > 100 Minimum quantity needed for Product 1 constraintAnd P1, P2, P3, P4 0 Non-negativity constraintsThe QM for Windows output for this problem is given below.Linear Programming Results:Variable Status ValueP1 Basic 100P2 NONBasic 0P3 Basic 220P4 NONBasic 0slack 1NONBasic 0slack 2Basic 160slack 3Basic 40surplus 4 NONBasic 0Optimal Value (Z) 34400Original problem w/answers:P1 P2 P3 P4 RHS DualMaximize 80 100 120 70Constraint 1 10 12 10 8 <= 3200 12Constraint 2 4 3 2 3 <= 1000 0Constraint 3 5 4 3 3 <= 1200 0Constraint 4 1 0 0 0 >= 100 -40Solution-> 100 0 220 0 Optimal Z-> 34400Ranging Results:Variable Value Reduced Cost Original Val Lower Bound Upper BoundP1 100 0 80 -Infinity 120P2 0 44 100 -Infinity 144P3 220 0 120 87.5 InfinityP4 0 26 70 -Infinity 96Constraint Dual Value Slack/Surplus Original Val Lower Bound Upper BoundConstraint 1 12 0 3200 1000 3333.333Constraint 2 0 160 1000 840 InfinityConstraint 3 0 40 1200 1160 InfinityConstraint 4 -40 0 100 0 120(b) Determine the slack (or surplus) value for each constraint and interpret its meaning.(b) Find the dual prices of the four constraints and interpret their meanings. What are the ranges in which each of these dual prices is valid?(c) If the profit contribution of Product 2 changes from $100 per unit to $130 per unit, what will be the optimal solution? What will be the new total profit? (Note: Answer this question by using the ranging results given above).(d) Which resource should be obtained in larger quantity to increase the profit most? (Note: Answer this question using the ranging results given above.).1 2 3 4 5To control the risk, the management of the company has specified that the total risk amount cannot exceed $200,000. In addition, the management wants to invest at least $150,000 in mutual fund 2 and at least $125,000 in mutual fund 3.With these restrictions, how much money should the portfolio manager of the company invest in each mutual fund so as to maximize the total annual return?(a) Define the decision variables.(b) Determine the objective function. What does it represent?(c) Determine all the constraints. Briefly describe what each constraint represents.Phone Door-to-Door____________________________________Morning $35 $60Evening $40 $70The Charity has 150 volunteer hours in the morning and 120 volunteer hours in the evening. Each phone contact takes 6 minutes and each door-to-door contact takes 15 minutes to conduct. The Charity wants to have at least 550 phone and at least 400 door-to-door contacts.Formulate a linear programming model that meets these restrictions and maximizes the total average donations by determining(a) The decision variables.(b) Determine the objective function. What does it represent?(c) Determine all the constraints. Briefly describe what each constraint represents.The firm also has three outlets with shortages of rental trucks, as follows:The firm wants to transfer trucks from those outlets with extras to those with shortages at the minimum total cost. The following costs of transporting these trucks from city to city have been determined:1 75 80 452 115 50 553 100 60 40For this transportation problem:(a) Define the decision variables.(b) Determine the objective function. What does it represent?(c) Determine all the constraints. Briefly describe what each constraint represents.