Plantco produces three products. Three workers work for Plantco, and the company must determine which product(s) each worker should produce. The number of units each worker would produce if he or she spent the whole day producing each type of product are given in Table 21. TABLE 21:

$$\begin{matrix} \text{ } & \text{Product}\\ \text{Worker} & \text{1} & \text{2} & \text{3}\\ \text{1} & \text{20} & \text{12} & \text{10}\\ \text{2} & \text{12} & \text{15} & \text{9}\\ \text{3} & \text{6} & \text{5} & \text{10}\\ \end{matrix}$$

The company is also interested in maximizing the happiness of its workers. The amount of happiness “earned” by a worker who spends the entire day producing a given product is given in Table 22. TABLE 22:

$$\begin{matrix} \text{Worker} & \text{Product}\\ \text{ } & \text{1} & \text{2} & \text{3}\\ \text{1} & \text{6} & \text{8} & \text{10}\\ \text{2} & \text{6} & \text{5} & \text{9}\\ \text{3} & \text{9} & \text{10} & \text{8}\\ \end{matrix}$$

Construct a trade-off curve between the objectives of maximizing total units produced daily and total worker happiness.

The Barron’s Big Money Poll asked 131 investment managers across the United States about their short-term investment outlook (Barron’s, October 28, 2002). Their responses showed 4% were very bullish, 39% were bullish, 29% were neutral, 21% were bearish, and 7% were very bearish. Let x be the random variable reflecting the level of optimism about the market. Set x = 5 for very bullish down through x = 1 for very bearish.

Develop a probability distribution for the level of optimism of investment managers.

Widgetco produces two types of widgets. Each widget is made of steel and aluminum and is assembled with skilled labor. The resources used and the per-unit profit contribution (ignoring cost of overtime labor purchased) for each type of widget are given in Table 20. Currently, 200 units of steel and 300 units of aluminum and 300 hours of labor are available. Extra overtime labor can be purchased for $10 per hour. Construct an exchange curve between the objectives of maximizing profit and minimizing overtime labor. TABLE 20:

$$\begin{matrix} \text{Resource} & \text{Type of Widget}\\ \text{ } & \text{1} & \text{2}\\ \text{Steel (lbs)} & \text{6} & \text{12}\\ \text{Aluminum (lbs)} & \text{8} & \text{20}\\ \text{Skilled labor (hours)} & \text{11} & \text{24}\\ \text{Profit contribution (\$)} & \text{500} & \text{1,100}\\ \end{matrix}$$

Evaluate the determinant.

$$\left| \begin{array} { r r } { - 1 } & { 2 } \\ { 3 } & { - 4 } \end{array} \right|$$

Add or subtract. Identify any x-values for which the expression is undefined.

$$\frac { 3 x + 2 } { x - 2 } - \frac { x + 5 } { x - 2 }$$

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. $3 \cdot 4^{x}+4 \cdot 2^{x}+8=0$

Explain how you can use the number line to compare the rational numbers for Anna and Mike.

How does the concept of hubris from Greek tragedy apply to the Peloponnesian War?

How would you say 'Ernest speaks with them' in Spanish?

A uniform flux density of 1 T is perpendicular to the plane of a five-turn circular coil of radius 10 cm. Find the flux linking the coil and the flux linkages. Suppose that the field is decreased to zero at a uniform rate in 1 ms. Find the magnitude of the voltage induced in the coil.

Gary has a function $s(x)=10^{x}$ and Amy has her function $a(m)=10^{m}$. Each person is going to choose a whole number at random from the numbers 1, 2, 3... 10, and substitute it into his or her respective function. After they do this, what is the probability that g(x)=a(m)?

$\Delta$ denotes the symmetric difference operator defined as $A\Delta B=(A\cup B)-(A\cap B)$, where A and B are sets. Is $\Delta$ commutative? If so, prove it; otherwise, give a counterexample.

A narrow beam of light containing red (660 nm) and blue (470 nm) wavelengths travels from air through a 1.00-cm-thick flat piece of crown glass and back to air again. The beam strikes at a $30.0^{\circ}$ incident angle. (a) At what angles do the two colors emerge? (b) By what distance are the red and blue separated when they emerge?

Determine the critical numbers of the given function and classify each critical point as a relative maximum, a relative minimum, or neither. $f(t)=2 t^{3}+6 t^{2}+6 t+5$