One constraint to a linear programming problem is $8 x_{1}+5 x_{2}+s_{2}=59$ This constraint determines a boundary line to the feasible region. (a) Is the point (3, 7) on the boundary line? (b) Can (2, 4) be in the feasible region?

We say that in network programming a socket should be at least bound to a local socket address. The first constructor of the DatagramSocket class in previous Table has no parameters. Can you explain how it is bound to the local socket address when used at the client site?

Name the four areas in which standards of ethical conduct exist for management accountants in the United States. What organization sets forth these standards?

Use the graphical method to solve each linear programming problem.

$$\begin{array}{lr} \text { Minimize } & z= 4 x+2 y \\ \text { subject to: } & x+y \leq 50 \\ & 2 x+y \geq 20 \\ & x+2 y \geq 30 \\ & x \geq 0 \\ & y \geq 0 \end{array}$$

Solve the linear programming problems using graphical methods. Restrict $x \geq 0$ and $y \geq 0$.

Maximize $f=x+4 y$ subject to

$$\begin{array}{rr} 7 x+3 y \leq 105 \\ 2 x+5 y \leq 59 \\ x+7 y \leq 70 \end{array}$$

Solve the linear programming problem. Assume $x \geq 0$ and $y \geq 0$.

Minimize $C=3 x+7 y$ with the constraints

$$\left\{\begin{array}{r} x+y \geq 9 \\ 3 x+4 y \geq 32 \\ x+2 y \geq 12 \end{array}\right.$$

J. Wold, project manager of Print Software, Inc., wants you to prepare a project network; compute the early, late, and slack activity times; determine the planned project duration, and identify the critical path. His assistant has collected the following information for the Color Printer Drivers Software Project:

Why would subcontractors for a government project want their activities on the critical path? Under what conditions would they try to avoid being on the critical path

Complete the problem.

To raise money, a service club has been collecting used bottles that it plans to deliver to a local glass company for recycling. Since the project began 80 days ago, the club has collected 24,000 pounds of glass for which the glass company currently offers 1 cent per pound. However, since bottles are accumulating faster than they can be recycled, the company plans to reduce by 1 cent each day the price it will pay for 100 pounds of used glass. Assuming that the club can continue to collect bottles at the same rate and that transportation costs make more than one trip to the glass company unfeasible, express the club's revenue from its recycling project as a function of the number of additional days the project runs. Draw the graph, and estimate when the club should conclude the project and deliver the bottles to maximize its revenue.

Solve the linear programming problems using graphical methods. Restrict $x \geq 0$ and $y \geq 0$.

Minimize $g=5 x+3 y$ subject to

$$\begin{array}{rr} 3 x+y \geq 12 \\ x+\ \ y \geq 6 \\ x+6 y \geq 11 \end{array}$$

Argile Textiles is evaluating a new product, a silk/wool blended fabric. Assume that you were recently hired as assistant to the director of capital budgeting, and you must evaluate the proposed project.

The fabric would be produced in an unused building located adjacent to Argile's Southern Pines, North Carolina, plant; Argile owns the building, which is fully depreciated. The required equipment would cost $200,000, plus an additional $40,000 for shipping and installation. With the new project, inventories would rise by $25,000, and accounts payable would increase by $5,000. All of these costs would be incurred at$t=0$. By a special ruling, the machinery could be depreciated under the MACRS system as 3-year property.

The project is expected to operate for four years, and then be terminated. The cash inflows are assumed to begin one year after the project is undertaken, or at$t=1$, and to continue to$t=4$. At the end of the project's life$(t=4)$, the equipment is expected to have a salvage value of $25,000.

Unit sales are expected to total 100,000 five-yard rolls per year, and the expected sales price is $2 per roll. Cash operating costs for the project (total operating costs excluding depreciation) are expected to amount to 60 percent of dollar sales. Argile's marginal tax rate is 40 percent, and its required rate of return is 10 percent. Tentatively, the silk/wool blend fabric project is assumed to be of equal risk to Argile's other assets.

You have been asked to evaluate this project and to make an accept/reject recommendation. To guide you in your analysis, your boss has asked you to answer the following set of questions.

(1) What is the regular payback period and the discounted payback period for the project?

(2) What is the rationale for the payback? According to the payback criterion, should Argile accept the project if the firm's maximum acceptable payback is two years?

(3) Explain the main difference between the regular payback and the discounted payback.

(4) What are the main disadvantages of the regular payback method? Is the payback method of any real usefulness in capital budgeting decisions?

You have signed a contract to build a garage for the Simpsons. You will receive a $500 bonus for completing the project within 15 working days. The contract also contains a penalty clause in which you will lose$100 for each day the project takes longer than 15 working days. Draw a project network given the information below. Complete the forward and backward pass, compute the activity slack, and identify the critical path. Do you expect to receive a bonus or a penalty on this project?

Consider the cash flows for the following investment projects:

$$\begin{array}{rrrrrr} &&&\text { Project's Cash Flow } \\ \boldsymbol{n} & \boldsymbol{A} & \boldsymbol{B} & \boldsymbol{C} & \boldsymbol{D} & \boldsymbol{E} \\ \hline 0 & -\$ 1.500 & -\$ 1.500 & -\$ 3,000 & 1.500 & -\$ 1.800 \\ 1 & \$ 1.350 & \$ 1.000 & \$ 1.000 & -\$ 450 & \$ 600 \\ 2 & \$ 800 & \$ 800 & \$ X & -\$ 450 & \$ 600 \\ 3 & \$ 200 & \$ 800 & \$ 1,500 & -\$ 450 & \$ 600 \\ 4 & \$ 100 & \$ 150 & \$ X & -\$ 450 & \$ 600 \end{array}$$

Assume that the MARR $=15 \%$.

(a) Suppose that projects A and B are mutually exclusive. Which project would be selected, based on the PW criterion?

(b) Suppose that projects D and E are mutually exclusive. Which project would you select based on the FW criterion?

(c) Find the minimum value of X that makes project C acceptable.

(d) Would you accept project D at $i=18 \%$ ?