Problem 1. Network Flow Optimization (10 points, Excel Solver or Frontline Solver is needed) You have collected three different types of fruits in a farm: grapes, peaches and bananas. You have a fleet of 4 trucks that you can use to ship fruits from the farm to the markets right away. The four trucks have different configurations (in terms of the suspension and the refrigeration) which lead to different amount of waste (loss) of fruit weights in the transporting process. The following table shows the loss as a percentage of weights along with the trucks capacities, the amount of fruits collected and the market prices that you can sell the fruits: Grapes Peaches Bananas Truck Capacity (tons) Truck 1 12% 10% 4% 40 Truck 2 12% 14% 5% 50 Truck 3 16% 17% 6% 55 Truck 4 18% 13% 8% 75 Fruit Collected (tons) 57 62 81 Market price ($/ton) 500 1,000 1,750

1.1 Draw a network flow diagram that helps to determine the shipping plan that will bring in the most sales revenue. You may draw the diagram below in Word or insert a photo of your hand-drawn diagram. Label your nodes, demand and capacity on the diagram (2 points) 1.2 Write out the detailed mathematical formulation for maximizing the total sales revenue. Please define the decision variables explicitly, show the objective function and all the constraints. You may use mathematical notation () but please define all parameters that you use. You may also write out the details if you prefer not to use this mathematical notation (3 points) 1.3 Setup the optimization problem in Excel. Please color the objective cell in red, decision variables in grey and given inputs in yellow. Label your worksheet as Problem 1.3 (3 points) Refer Excel 1.4 What is the optimal shipping plan (which truck brings which fruits and how much)? What is the optimal (maximum) total sales revenue? Write down your answers below (1 point) 1.5 If your objective is to maximize the total tons of fruits brought to the markets (instead of total sales revenue as above), how would you modify the model to get the optimal solution? Please indicate how you will modify the original mathematical formulation for this purpose. You dont need to setup the model in Excel (1 point)