all steps please! questions a-f

Given: Five bulldozers are available for an earthwork job that will require the dozing of 130,000 bcy of soil. Information for each bulldozer is presented below. The client's son drives the D3, so you have to use it at least 20 hours. You can use each machine for the maximum hours stated. If you wish to run overtime, each machine costs 1.5 times the normal rate, but you can get each of the machines for another 50 hours. Bulldozer D3 814S No. 1 814S No.2 D7G-7U D9N-9U Production Cost of Normal Rate, bcy/hr Operation, $/hr 40 $45.55 175 $98.25 175 $98.25 275 $127.16 500 $215.80 Maximum Hours 200 150 130 100 100 Find: Express mathematically your objective function and all constraints. Define your decision variables. b. Is it possible (not necessarily optimum) to finish the project without using overtime? If so, what is the duration that can be achieved without overtime at minimum cost (including using the D3 for at least 20 hours)? What are the minimum cost, and corresponding allocation of resources (including the use of overtime)? d. How does the requirement of using the owner's son affect the optimum solution to part c? Hint: What would happen to your solution and cost if you were not required to use him at all? What is the shortest possible duration for moving the 130,000 bcy, disregarding cost? f. Extra credit (3 points): If you finish faster than 140 hours, you get a bonus of $250/hour for every hour under 140 hours. If you run longer than 150 hours, you are penalized $500/hour for each hour over 150. What is your optimal solution now