Able Widgets has a factory

1) Able Widgets has a factory that produces three types of widgets, types 1, 2, and 3, on a make-to-order basis. The factory operates five days a week for 9 hours each day. The key decision is what type of machine should be used to process each widget during the coming quarter (13 weeks). Two types of machines can be used: advanced and regular. Advanced machines can be used to make all widgets and are the only machines that can produce certain widgets, such as “The moving widgets.” Demands, variable costs for each type of machine, and production rates on the machines are given in the table below.Widget Demand Advanced machine capacity(Widget/hour) Regular machine capacity(Widget/hour) Machine cost($/Widget) Outsourcing Cost($/Widget)1 90,00 9.4 0 $1.30 $1.702 153,00 10.4 10.4 $1.22 $1.503 20,00 8.8 8.8 $1.00 $1.30The factory has 30 regular machines and 6 advanced machines. After manufacturing, the widgets are sent to the finishing department and then sold. Any widget that cannot be manufactured in the factory because of limited capacity will be purchased from an external supplier, finished at the factory, and sold at the market selling price.If Ai, Ri, and Pi (where i = 1, 2, 3…) are used to denote the number of widgets to be produced on advanced machines, the number of widgets to be produced on regular machines, and the number of widgets purchased from an outside supplier respectively,a) Determine the objective function for the data given above.b) Write out the constraints that meet production requirements.c) Determine the constraint on available production time on advanced machines.d) Determine the constraint on available production time on regular machines.2) The following spreadsheet shows ferry pricing model. Use the spreadsheet to answer the question(s) below.A B1 Airline Pricing Model 2 3 Data 4 Ferry capacity 2405 Fixed Cost $60,0006 Demand Function 7 Slope -2.408 intercept 1,6009 10 Model 11 12 Revenue 13 14 Unit Price $400.0015 Demand 16 Number of trips/day 17 Total revenue 18 Cost 19 Fixed Cost 20 21 Profit (a) Fill in the spreadsheet(b) Use your spreadsheet to determine the profit maximizing number of trips per day. How much profit does the ferry company earn at the optimal level you selected?