Question 1. Suppose P =x+ 2y is the objective function (Profit function) in a linear programming (maximization) problem, where x is the number of units of product A and y is the number of units of product B. a) What does the coefficient of x represent? How about the coefficient of y? (4 marks) b) Given the linear programming problem: x+ys4 Resource 1 and 3x+yS7 Resource2 c)What is the linear inequality that represents "" unit increase in Resource 1? (2 marks) d) Using the iso-profit line approach, find the optimal solution to the above linear programming problem. (2 marks)

Question no. 2) a) Find the solution set for the following systems graphically and graph the iso profit line on the same diagram. (8 marks) b) Using the iso-profit line, determine the optimal solution to each system. (2 marks) C) Which constraints are binding, and which ones are non-binding ? (5 marks) C +3y S.t. 4x + 2y2 12 3x+ 5y 2 25 ) P=2x+y S.t. X+ 3y s9 5X+2ys 15 Zx+ 3y S 10 x20 and y20 X20 y20

Question no. 3) Explain the meaning of shadow pricing and binding constraints in your own words. (5 marks)

Question no. 4) Consider the following linear programing problem: P 2x +3y subject to 2x +5y s 25 Resource 1 3x+2ys 19 Resource 2 as well as x20 and y 20. a) Use the method of corners (showing your graph and corner points) to solve this problem. . Find the number of x and y so that P is optimized) (5 marks) b) Will the optimal solution you found in part "a" remain optimal if coefficient of x changes to 1 in the "objective function"? How do you know? (3 marks) c)Will the solution remain optimal is amount of Resource 2 changes to 20? How do you know? (2 marks)

Question 5 - Formulate the following LP problems (Do not attempt to solve): a) Soundex produces two models of satellite radios. Model A requires 13 min of work on assembly line 1 and 9 min of work on assembly line 2. Model B requires 8 min of work on assembly line 1 and 11 min of work on assembly line 2. At most, 25 labor-hours of assembly time on line 1 and 22 labor-hours of assembly time on line 2 are available each day. It is anticipated that Soundex will realize a profit of $10 on model A and $12 on model B. How many satellite radios of each model should be produced each day to maximize Soundex's profit? (5 marks) b) Patricia has at most $40,000 to invest in securities in the form of corporate stocks. She has narrowed her choices to two groups of stocks: growth stocks that she assumes will yield a 18% return (dividends and capital appreciation) within a year and speculative stocks that she assumes will yield a 23% return (mainly in capital appreciation) within a year. Determine how much she should invest in each group of stocks to maximize the return on her investments within a year if she has decided to invest at least 2 times as much in growth stocks as in speculative stocks. (5 marks)

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kindly give the full answers of every question.