Well shown calculations please

EA 452 Quantitative Analysis Final Exam SBI'IBIH'II'I'I! to Constants Question 2. The Ford Motor Company makes cars and trucks on an assembly line. Each car and truck requires labor and needs to visit three stations: engine installation, hood installation, and wheel installation. The hours of labor and hours required at each station are as follows: Engine Hood Wheel Vehicle Labor Installation Installation Installation lGar 4 4 3 Truck 3 8 5 4 There are available 12 hours of labor, 48 hours of engine installation. 20 hours of hood installation. and 12 hours of wheel installation. Labor oosts $20 per hour, and each installation station costs $10 per hour to operate. Cars sell for 3?\") each, and thcks sell for $530 each. a. Formulate and graphically solve for the recommended production quantities. Do not require production units to be integers. b. How much should Ford be willing to pay to another potential worker {Joe} to supply one more unit of labor. {Joe is not part of the 12 hours of labor mentioned above.) Make or Buyr with Fixed Costs Question 3. Danchuk Manufacturing produces a variety of classic automobiles. including a 1955 Chevy and a 1955 Thunderbird. Each car consists of three components that can be manufactured by Danchuk: a body, an interior, and an engine. Both cars use the same engine, but different bodies and different interiors. Danchuk's sales forecast indicates that EDD Chews and 50D Thunderbirds will be needed to satisfy demand during the next year. Because only 20-00 hours of in-house manufacturing time is available, Danchulr. is considering purchasing some, or all, of the components from outside suppliers. If Denchuk manufactures a component in-house, it incurs a fixed setup cost as well as a variable manufacturing cost. The following table shows the setup cost, the manufacturing time per component, the manufacturing cost per component, and the cost to purchase each of the components from an outside supplier: Manufacturing Purchase Setup Cost Manufacturing |Dost per Unit lCost per Unit (thousands Time per Unit [thousands of (thousands Corn - onent of dollars hours dollars of dollars Formulate a linear program for Denohult to minimize total cost to meet the sales forecasts. But you need not compute an optimum. EA 452 Quantitative Analysis Final Exam Economic Analysis with Teamwork Question 4. Food on Foot operates a weekly meal program everirIr Sunday in Hollywood- They are considering three alternative distribution systems. Arrivals to the distribution stand follow the Poisson distribution with an average of one homeless person arriving every 12 minutes. The cost for a homeless person waiting is $2 per hour. The first system involves one volunteer (who talks to the homeless and serves food and serves drinks) and costs $10 per hour to operate [the opportunity cost of the volunteer's time}, and it has an exponential service rate, and it can serve an average of one homeless person every 6 minutes. The second system involves two volunteers working as a team {one talks to the homeless and serves food. and the other serves drinks} and costs $20 per hour to operate (the opportunity cost of the 2 volunteer's time). and it has an exponential service rate. and it can serve an average of one homeless person everyIr 3 minutes. The third system involves three volunteers working as a team {one talks to the homeless. one serves food, and the third serves drinks} and costs $30 per hour to operate {the opportunity cost of the 3 volunteer's time), and it has an exponential service rate. and it can serve an average of one homeless person every 1 minute. Which system should be chosen\"? Rte-compute your answer if the customers value their time at $20 per hour, rather than $2 per hour. You may use any or all of the following analytical formulas for an MM1 system to compute your answer: The probability of no units in the system: P.) = 1-:up The average number of units in the waiting line: L, = Pitfall-1}} The average number of units in the system: L = f.ET + tip The average time a unit spends in the waiting line: WE, = Ly}: The average time a unit spends in the system: w = fife-It} The probability that an arriving unit has to wait: PW = Mp Probability of n units in the system: F'n = {Morin}, BA 452 Quantitative Analysis Final Exam Backward Induction Question 5. Use backward induction (and draw a decision tree, if needed) to help make the following sequential decisions, where later decisions depend on earlier decisions: 1. Should the Bayer Biological Products Group spend $20 million to begin preclinical development of a new blood-clot-busting drug? a. The probability of successful testing on humans is 0.7 b. If the testing is not successful, the project is terminated c. If the testing is successful, the project requires $2 million to file a license with to the FDA. The probability of successful filing 0.9 d. If the filing is successful,, demand and revenues are uncertain: i. With probability 0.4, demand is low and revenue is $60 million. ii. With probability 0.1, demand is medium and revenue is $80 million. iii. With probability 0.5, demand is high and revenue is $100 million. 2. If the testing on humans were successful, should the Bayer Biological Products Group sell its rights in the project for $70 million? Compute expected profit for the Bayer Biological Products Group