business decision analysis

Requirements: mathematics 1. retail store in Surrey, BC, receives shipments of a particular product from Hong Kong and Macau. Let x = units of the product received from Honk Kong and y = units of the product received from Macau a) Write an expression for the total units of the product received by the retail store in Surrey. (2 marks) b) Shipments from Hong Kong cost $0.25 per unit, and shipments from Macau cost $0.35 per unit. Develop an objective function representing the total cost of shipments to Surrey. (2 marks) c) Assuming the monthly demand at the retail store is 7500 units, develop a constraint that requires 7500 units to be shipped to Surrey. (2 marks) d) No more than 4500 units can be shipped from Hong Kong and no more than 3000 units can be shipped from Macau in a month. Develop constraints to model this situation. (2 marks) e) Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model for satisfying the demand at the Surrey retail store at minimum cost. (2 marks). 2. Preliminary plans are underway for the construction of a new stadium for a major league baseball team. City officials question the number and profitability of the luxury corporate boxes planned for the upper deck of the stadium. Corporations and selected individuals may purchase a box for $250,000. The fixed construction cost for the upper-deck area is estimated to be $5,400,000, with a variable cost of $100,000 for each box constructed. a. What is the breakeven point for the number of luxury boxes in the new stadium? (4 marks) b. Preliminary drawings for the stadium show that space is available for the construction of up to 60 luxury boxes. Promoters indicate that buyers are available and that all 60 could be sold if constructed. What is your recommendation concerning the construction of luxury boxes? What profit is anticipated? (4 marks) 3) Financial Analysts, Inc., is an investment firm that manages stock portfolios for a number of clients. A new client has requested that the firm handle an $800,000 portfolio. As an initial investment strategy, the client would like to restrict the portfolio to a mix of the following two stocks: Let x = number of shares of Oil Alaska y = number of shares of Southwest Petroleum
Stock Price per share Estimated Annual return per Share
Oil Alaska $65 $8.5
Southwest Petroleum $45 $4.0 a. Develop the objective function, assuming that the client desires to maximize the total annual return. (6 marks) b. Show the mathematical expression for each of the following three constraints: (9 marks) (1) Total investment funds available are $750,000. (2) Maximum Oil Alaska investment is $600,000. (3) Maximum Southwest Petroleum investment is $550,000. c. Could either of x or y be negative? Why? What mathematical expression(s) would guarantee that? (3 marks) 4. Graph the following lines and identify the slope, y-intercept and x-intercept of each line (16 marks)
3x + 5y – 12 = 0
-4x -6y + 10 = 4
3/4 x + 2/5 y – 6 = 0
2y + 3x = -3 3x + 5y – 12 = 0 -4x -6y + 10 = 4 3/4 x + 2/5 y – 6 = 0 2y + 3x = -3