4) Formulate the following LP problems (define the variables, write the objective function and constraints including the non-negativity ones if any. Do not attempt to solve): a) Soundex produces two models of satellite radios. Model A requires 12 min of work on assembly line 1 and 7 min of work on assembly line 2. Model B requires 9 min of work on assembly line 1 and 10 min of work on assembly line 2. At most, 35 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 $17 on model A and $19 on model B. How many satellite radios of each model should be produced each day to maximize Soundexs profit? (6 marks)

b) Patricia has at most $45,000 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 14% return (dividends and capital appreciation) within a year and speculative stocks that she assumes will yield an 18% 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. (6 marks)