TraNSPoRTATION Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type-A vessel has 60 deluxe cabins and 160 standard cabins, whereas a type-B vessel has 80 deluxe cabins and 120 standard cabins. Under a charter agreement with Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 360 deluxe and 680 standard cabins for their 15 -day cruise in May. It costs \(\$ 44,000\) to operate a type-A vessel and \(\$ 54,000\) to operate a type-B vessel for that period. How many of each type vessel should be used in order to keep the operating costs to a minimum?

Patricia has at most \(\$ 30,000\) 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 \(15 \%\) return (dividends and capital appreciation) within a year and speculative stocks that she assumes will yield a \(25 \%\) return (mainly in capital appreciation) within a year. Determine how much she should invest in each group of stocks in order to maximize the return on her investments within a year if she has decided to invest at least 3 times as much in growth stocks as in speculative stocks.

Soundex produces two models of satellite radios. Model A requires 15 min of work on assembly line I and 10 min of work on assembly line II. Model B requires 10 min of work on assembly line I and 12 min of work on assembly line II. At most \(25 \mathrm{hr}\) of assembly time on line I and \(22 \mathrm{hr}\) of assembly time on line II are available each day. Soundex anticipates a profit of \(\$ 12\) on model \(A\) and \(\$ 10\) on model \(B\). Because of previous overproduction, management decides to limit the production of model A satellite radios to no more than \(80 /\) day. a. To maximize Soundex's profit, how many satellite radios of each model should be produced each day? b. Find the range of values that the contribution to the profit of a model A satellite radio can assume without changing the optimal solution. c. Find the range of values that the resource associated with the time constraint on machine I can assume. d. Find the shadow price for the resource associated with the time constraint on machine \(\mathrm{I}\). e. Identify the binding and nonbinding constraints.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The problem $$ \begin{aligned} \text { Minimize } & C=2 x+3 y \\ \text { subject to } & 2 x+3 y \leq 6 \\ & x-y=0 \\ & x \geq 0, y \geq 0 \end{aligned} $$ is a linear programming problem.

Find the graphical solution of each inequality. $$ y \geq-1 $$

Determine graphically the solution set for each system of inequalities and indicate whether the solution set is bounded or unbounded. $$ \begin{array}{l} 4 x-3 y \leq 12 \\ 5 x+2 y \leq 10 \\ x \geq 0, y \geq 0 \end{array} $$