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A repair person fixes broken televisions. The repair time is exponentially distributed with a mean of 30 minutes. Broken televisions arrive at his repair shop according to a Poisson process, on average 10 broken televisions per 8 hour day. Answer the following parts (i), (ii), & (iii) in two different ways: (A) Using steady state queuing theory (you can assume that the repair person stays/ works at the shop forever, never takes any breaks, and has an infinite storage location for broken televisions (if necessary).The 4M company has a work center with a single turret lathe. Jobs arrive at this work center according to a Poisson process at a mean rate of 2 jobs per day. The lathe processing time has an exponential distribution with a mean of 0.25 days per job. a.) On average, how many jobs are waiting in the work center? b.) On average, how long will a job stay in the center? c.) Since each drop takes a big space, the waiting jobs are currently waiting in the warehouse. The production manager is proposing to add a storage space near the lathe. If an arriving job will have at least 90% chance of waiting near the lathe, how big should be the storage space near the lathe? - Queuing Theory Problem - Please solve parts a.), b.), and c.) and show all the steps to get to the final solution(s).E AaBbCel AaBbCcl AaBbCc[ AaBbCc AaBbCc Heading 2 1 Normal 11 No Spac.. Heading 1. Heading Paragraph Styles Hint: Utilize queuing theory Problem 4 As Operations Manager, you would like to know which product mix needs to be manufactured. The firm manufactures two models of the trans catheter aortic valve replacement system: the system which is equipped with 23 mm valves and the system which is equipped 29 mm valves. The expected profit for 23mm system is $300 per unit, while profit for 29mm system is $360 per unit. The firm utilizes aortic valves bought from an external supplier. There is a supply restriction for both of 23 mm and 29mm valves. The current suppler of valves cannot supply more than 300 units of 23 mm valves per week and no more than 600 units of 29 mm valves per week. The manufacturing time for one 23 mm aortic valve system is 1.6 hours per week. The manufacturing time for one 29 mm aortic valve system is 1.8 hours per week. There are 1520 hours of total manufacturing time available per week. Determine how many units of 23 mm aortic valve system and 29 mm aortic valve system the firm needs to manufacture per week to maximize profit. Hint: Set up and solve the problem as Linear or Integer Programming problem using Excel OM, POM, or Solver. W 12 WE hp 9 OSolve the following queueing theory problems. Submit your complete solutions 1. The Metro Rail Transit {M HT] is considering opening a new window counter for elderly, handicapped and student discount transactions. Based on the records, management estimates that customers will arrive at a Poisson distribution with a rate of 15 customers per hour. The service attendant who will be assigned can service the customers follows an exponential distribution at a rate of one every three minutes. Find the following: [a] Probability that the service facility is empty [b] The percentage {or probability] of time that the service attendant is accommodated [c] Average number in the waiting line [d] Average number in the system [e] Average waiting time in the queue if] Average waiting time in the system Problems 1. Suppose a monopolistic local utility company faces a demand curve given by P = 120 4Q. Total cost for this film is given by TC = 400 + 4Q, and MC is fixed at $4 per unit. 2. a b. c. d. e. f. Does the technology of a firm represent economies of scale? What is the fixed cost? Does this indicate high barriers to entry? 'What is the socially optimal level of production and price? Suppose this industry operates as a monopoly. Find the equilibrium price and quantity. The government, bowing to public pressure to regulate monopolies, decides to force rms to charge their marginal cost just like they would in perfect competition. How much will the monopolist produce? 1What is the profit for this monopolist? Is it sustainable? Suppose the government instead chooses to force the monopolist to charge a price equal to their average total cost, this monopolist will supply 25 units. What will be their profits? Plastic molding has both industrial and dental uses. Consider a monopolist producer of this good with constant marginal cost MC = 4. The demand curves for the two market segments are given below p Dental users: P = 100 2Q Industry users: P = 50 0.552 If a monopolist can practice thirddegree price discrimination, what price will they set in the two markets? 1What is the consumer surplus for each market? Now suppose the monopolist caimot price discriminate. Instead, they must charge a single price in both markets. What price will they charge? ls consumer surplus higher or lower without price discrimination? (True story} Facing a market like this, one supplier of the plastic molding methyl methacrylate considered mixing arsenic with the product sold to industrial users. You might think about why this could be advantageous to the seller. Problems 1. A monopoly faces a market demand curve given by P = 42 Q. Its marginal cost cmve is given by MC: Q. wrongs-s What 1s the equation for the marginal revenue? Show this on a graph. Find the profitmaximizing level of production for this monopolist. What price will the monopolist charge? TWhat price and quantity would be socially optimal? What is this monopolist' s total revenue? Graph the producer surplus, the consumer surplus, and the deadweight loss for the market with the monopolist. 2. True or False: A monopolist can always make a positive profit. '3. True or False: A firm in perfectly competitive market will always earn zero economic profit. 4. Suppose a monopolistic local utility company faces a demand curve given by P = 120 4Q. Total cost for this firm is given by TC = 400 + 4Q, and MC is fixed at $4 per unit. a. . TWhat is the fixed cost? Does this indicate high barriers to entry? b c. d. e f. Does the technology of a firm represent economies of scale? What is the socially optimal level of production and price? Suppose this industry operates as a monopoly. Find the equilibrium price and quantity. The government, bowing to public pressure to regulate monopolies, decides to irce rms to charge their marginal cost just like they would in perfect competition. How much will the monopolist produce? What is the profit for this monopolist? Suppose the government instead chooses to force the monopolist to charge a price equal to their average total cost, this monopolist will supply 25 units. What will be their profits
