can use excel

Problem 2 Albert and Ben are two carpenters who are hired to work in a house renovation project, but they must decide on the tasks to specialize on. There are three main tasks: (1) Bathroom (2) Kitchen (3) Basement They are paid to complete the job on-time, but they get paid extra if they develop a task on their own (because they can showcase their expertise like that). They are paid $50 per hour. If they work alone, they will be paid $100 extra for the bathroom, $200 extra for the kitchen, and $250 extra for the basement. It takes 12 labor-hours to finish the bathroom, 20 labor-hours to finish the kitchen, and 24 labor-hours to finish the basement. They have only 24 hours to finish the job. a) What would be their first choice such that it maximizes their income? To answer the question, construct the pay-off matrix of the game and find the non-cooperative solution of the game. Calculate the profit based on the immediate task that they are about to make. Hint: To guide you through the construction of the pay-off matrix, I am providing you the following example. If Albert chooses Bathroom and Ben chooses Kitchen, Albert will take 12 hours to finish the bathroom so he will gain $50*12+$100 = $700, while Ben will take 20 hours to finish the kitchen so he will gain $50*20 +$200=$1200. If, for example, Albert and Ben both choose Kitchen, then they have to divide the task among them, so each will work 10 hours and they won't get the extra money. That means, they will each gain $50*10= $500 b) Suppose a third carpenter, Clark, came along and he would be able to help finish the job. Thus, they decide to cooperate among the three carpenters. If A stands for Albert, B stands for Ben and C stands for Clark, the expected payoffs for each coalition would be: V({A})=950, V({B})=900, V[{C})=900, V({A,B}}=2000, V({B.C})=2000, V[{A,C})=1900, V({A,B,C})=3350. How would the carpenters share their revenue if they decided to cooperate? Use the Shapley Value or the core of the Game to solve this