Q2 (a): Given the following demand and supply function for three competing products, qai = 46...

  

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Q2 (a): Given the following demand and supply function for three competing products, qai = 46 – 10p, + 2p2 + 2p3 9s1 = 12p, - 16 qaz = 30 + 2p1 - 6p2 + 4p3 4s2 = 6pz - 22 9as = 38 + 2p, + 4p2 - 8p3 4s3 = 6p2 - 10 Determine whether there are prices which bring the supply and demand levels into equilibrium for each of the three products. If so, what are the equilibrium quantities? (05] %3D [Use Cramer's rule to solve the system of linear equations.] Q2 (b): A car leasing agency purchases new cars each year for use in the agency. The car cost $16,000 now. They are used for 4 years, after which they are sold for $3,600. The owner of the ageney estimated that the variable cost of operating the cars, exclusive of gasoline, are $0.26 per mile. Cars are leased at a flat rate of $0.43 per mile (gasoline not included). (04] (i) What is the break-even mileage for the 4 years period? (ii) What are total revenue, total cost and total profit for the 4 year period if a car is leased for 55,000 miles? (iii) What price per mile must be charged in order to break even if a car is leased for 55,000 miles over a period of 4 years? (iv) What price per mile must be charged in order to earn a profit of $5,000 per car over 4 year lifetime if it is leased for a total of 55,000 miles? Q2 (c): Give any two daily life examples of linear programming. [01] Q2 (a): Given the following demand and supply function for three competing products, qai = 46 – 10p, + 2p2 + 2p3 9s1 = 12p, - 16 qaz = 30 + 2p1 - 6p2 + 4p3 4s2 = 6pz - 22 9as = 38 + 2p, + 4p2 - 8p3 4s3 = 6p2 - 10 Determine whether there are prices which bring the supply and demand levels into equilibrium for each of the three products. If so, what are the equilibrium quantities? (05] %3D [Use Cramer's rule to solve the system of linear equations.] Q2 (b): A car leasing agency purchases new cars each year for use in the agency. The car cost $16,000 now. They are used for 4 years, after which they are sold for $3,600. The owner of the ageney estimated that the variable cost of operating the cars, exclusive of gasoline, are $0.26 per mile. Cars are leased at a flat rate of $0.43 per mile (gasoline not included). (04] (i) What is the break-even mileage for the 4 years period? (ii) What are total revenue, total cost and total profit for the 4 year period if a car is leased for 55,000 miles? (iii) What price per mile must be charged in order to break even if a car is leased for 55,000 miles over a period of 4 years? (iv) What price per mile must be charged in order to earn a profit of $5,000 per car over 4 year lifetime if it is leased for a total of 55,000 miles? Q2 (c): Give any two daily life examples of linear programming. [01]