The Programming Example, Converting a Number from Decimal to Binary, in Chapter 15, contains a program that uses recursion to convert a decimal number into an equivalent binary number. Write a program that uses a stack to convert a decimal number into an equivalent binary number.

The Program, Converting a Number from Decimal to Binary, contains a program that uses recursion to convert a decimal number into an equivalent binary number. Write a program that uses a stack to convert a decimal number into an equivalent binary number.

Solve the linear programming problems stated. Maximize $P=20 x+30 y$ subject to

$$\begin{aligned} 0.6 x+1.2 y & \leq 960 \\ 0.03 x+0.04 y & \leq 36 \\ 0.3 x+0.2 y & \leq 270 \\ x, y & \geq 0 \end{aligned}$$

Create an interesting scenario leading to the following linear programming problem: Minimize c=10x+10y subject to

$$\begin{array}{l}{20 x+40 y \geq 1,000} \\ {30 x+20 y \geq 1,200} \\ {x \geq 0, y \geq 0.}\end{array}$$

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

Maximize $C=2 x+6 y$ with the constraints

$$\left\{\begin{array}{r} x+y \leq 12 \\ 3 x+4 y \leq 40 \\ x+2 y \leq 18 \end{array}\right.$$

One constraint to a linear programming problem is $6 x_{1}+4 x_{2}+s_{1}=24$. This constraint determines a boundary line to the feasible region. (a) Is the point (3, 5) on the boundary line? (b) Can (3, 5) be in the feasible region?

Each Apple retail store has several departments. Why is it useful for its management to (b) treat each department as a profit center?

As per the continuation of the previous problem. Assume it costs $\$ 300$ per mile to run cable on land but $\$ 500$ per mile to lay it under water. a. Assume $C$ is the total cost of the project, in dollars. Describe why $C=300 L+500 \mathrm{~W}$. b. Write a formula for $C$ as a function of $L$. (Hint: Use part of the previous problem.) c. Find the amount of cable that runs under water and the total cost of the project if you choose $L$ to be 1 mile long. Draw and properly label a picture that shows this cable plan. d. Find the amount of cable that runs underwater and the total cost of the project if you choose $L$ to be 3 miles long. Draw and properly label a picture that shows this cable plan. e. Draw a graph of the cost $C$ as a function of $L$, and describe what the graph is showing. f. What value of $L$ gives the least cost for the project? g. Determine the value of $W$ that corresponds to your answer in part $\mathrm{f}$, and draw a picture showing the least-cost project. h. Potential legal disputes about easements have caused the cost of laying cable on land to increase to $\$ 700$ per mile. With this change, find a new formula for the cost $C$. How does this affect your plans for the least-cost project?

Solve the linear programming problem Minimize $\quad C=30 x+10 y$ subject to

$$\begin{aligned} 1.8 x+0.9 y & \geq 270 \\ 0.3 x+0.2 y & \geq 54 \\ 0.01 x+0.03 y & \geq 3.9 \\ x, y & \geq 0 \end{aligned}$$

Why was Patio Grill Company's management being misled by the traditional product-costing system? What mistakes were being made?

Use the graphical method to solve each linear programming problem.

$$\begin{array}{lr} \text { Maximize } & z=2 x+4 y \\ \text { subject to: } & 3 x+2 y \leq 12 \\ & 5 x+y \geq 5 \\ & x \geq 0 \\ &y \geq 0 \end{array}$$

The hexadecimal numeration system, used in computer programming, is a base sixteen system that uses the symbols $0,1,2,3,4,5,6,7,8,9$, $A, B, C, D, E,$ and $F.$ Change each of the following hexadecimal numerals to base ten numerals.

b. $1 \mathrm{C} 2 \mathrm{~B}_{\text {sixteen }}$

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

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

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

Elizabeth Jablonski is the director of Research and Development for Galaxy Electronics. Last week, she submitted the following funding request as part of the annual budget process.

The aircraft guidance system is a project the company has publicly announced and is marketing strongly to manufacturers. The miniature DVD project has received little support in the company but is one of Elizabeth’s favorites. The chief fi nancial offi cer requests all groups to revise their budgets because of lower than expected sales for the company. Department heads have been asked to submit new budgets that are 10 percent below their original submissions.

Learning the company’s commitment to the aircraft guidance system, Elizabeth submits the following revision noting that it is 10 percent lower as requested.

Required
Is Elizabeth likely to be successful in achieving the goal you identified in the previous requirement?