Group members should choose a particular field of interest. Research how linear programming is used to solve problems in that field. If possible, investigate the solution of a specific practical problem. Present a report on your findings, including the contributions of George Dantzig, Narendra Karmarkar, and L. G. Khachion to linear programming.

Write expression using a variable for the area and perimeter of a rectangle with length

$$2 x + 7$$

and width

$$2 x - 7$$

.

Evaluate the expression. (49 - 11)/(12 + 7)

Determine the best method to solve the system of equation. Then solve the system. 3x - 4y = -5, -3x + 2y = 3

Simplify by combining like terms. $2(h+2 g)-(g-h)$

The values of a period $2 \pi$ function $f (t)$ in one full period are given. Sketch several periods of its graph and find its Fourier series.

$$f ( t ) = \left\{ \begin{array} { l l } { 0 , } & { - \pi \leqq t \leqq 0 } \\ { \sin t , } & { 0 \leqq t \leqq \pi } \end{array} \right.$$

Construct the confidence interval estimate of the mean. Listed below are the amounts of net worth (in millions of dollars) of these ten wealthiest celebrities: Tom Cruise, Will Smith, Robert De Niro, Drew Carey, George Clooney, John Travolta, Samuel L. Jackson, Larry King, Demi Moore, and Bruce Willis. Construct a 98% confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required?

$$\begin{array} { c c c c c c c c c } { 250 } & { 200 } & { 185 } & { 165 } & { 160 } & { 160 } & { 150 } & { 150 } & { 150 } & { 150 } \end{array}$$

Solve the heat equation $k u_{x x}=u_{t}, 0<x<1$, $t>0$ subject to the given conditions.

$$\begin{array}{l}{u(0, t)=100, \quad u(1, t)=100} \\ {u(x, 0)=0}\end{array}$$

The number of microwave ovens that manufacturers produce depends on price. The higher the price, the more microwaves manufacturers will produce. The equation that relates price to the number of microwaves produced at that price is called a supply equation. If the supply equation for a 2-cubic-foot counter top microwave is

$$p = \frac { 1 } { 10 } q + 130$$

, where p is the price and q is the number of microwaves produced for sale at that price, how many of that model microwave will be produced if the price is $150?

Determine whether the statement is true or false. If $w$ is the closest vector in a subspace $W$ of $R^n$ to a vector $v$ in $R^n$, then $w$ is the orthogonal projection of $v$ on $W$.

Find the product.

$$( - 5 g - 2 h ) ( - 5 g + 2 h )$$

Let $A$ be an abelian group and let $D$ be the (diagonal) subgroup $\{(a,a)\ | \ a\in A\}$ of $A\times A$. Prove that $D$ is a normal subgroup of $A\times A$ and $(A\times A)/ D \cong A$.

A physics student in the class recalled that the period of a pendulum should be proportional to the square root of its length. Use this information to suggest a transformation that should achieve linearity. Then carry out your transformation.

Consider a redox reaction for which

$$E ^ { \circ }$$

is a negative number. Can an electrochemical cell based on this reaction accomplish work on its surroundings?