Productco produces three products. Each product requires labor, lumber, and paint. The resource requirements, unit price, and variable cost (exclusive of raw materials) for each product are given in Table 70. Currently, 900 labor hours, 1,550 gallons of paint, and 1,600 board feet of lumber are available. Additional labor can be purchased at $6 per hour, additional paint at$2 per gallon, and additional lumber at $3 per board foot. For the following two sets of priorities, use preemptive goal programming to determine an optimal production schedule. For set 1: Priority 1: Obtain profit of at least$10,500. Priority 2: Purchase no additional labor. Priority 3: Purchase no additional paint. Priority 4: Purchase no additional lumber. For set 2: Priority 1: Purchase no additional labor. Priority 2: Obtain profit of at least $10,500. Priority 3: Purchase no additional paint. Priority 4: Purchase no additional lumber. TABLE 70:

$$\begin{matrix} \text{Product} & \text{Labor} & \text{Lumber} & \text{Paint} & \text{Price (\$)} & \text{Variable Cost (\$)}\\ \text{1} & \text{1.5} & \text{2} & \text{3} & \text{26} & \text{10}\\ \text{2} & \text{3} & \text{3} & \text{2} & \text{28} & \text{6}\\ \text{3} & \text{2} & \text{4} & \text{2} & \text{31} & \text{7}\\ \end{matrix}$$

A map of the United States has a scale of 1 in. : 250 mi. How far apart are the cities on the map?

How much should the United States rely on nuclear power as a source of energy? Explain your view.

The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the truth or falsity of the premises and conclusion. Finally, determine whether the argument is sound or unsound. Chicago is a city in Michigan and Michigan is part of the United States. Therefore, Chicago is a city in the United States.

If the United States had been poor in natural resources, how would industrialization have been affected?

Why does Rogers think that the GROWS landfill is “aptly named” (5)? What connotations do you think Waste Management Inc. intended the name GROWS to have? What connotations does Rogers think the name has?

In the following, name the term defined or answer the question.

A firm wants to justify smaller lot sizes economically. Management knows that it cannot change the cost to carry one unit in inventory because this is largely based on the value of the item. To justify a

Find the cardinality of each of the following sets. For some exercises you may need to consult a reference, such as the Internet or an encyclopedia. J=the set of all states of the United States that border Minnesota

For the following term or person, write a sentence explaining its connection to the new United States: Lewis and Clark

[Related to the Apply the Concept on page 828] If real GDP in the United States declined by more during the 2007– 2009 recession than did real GDP in Canada, China, and other trading partners of the United States, would the effect be to increase or decrease U.S. net exports? Briefly explain.

a. Use the two points for white non-Hispanics to find an equation in the form $y=m x+b$ that models the percentage of white non-Hispanics, $y$, in the United States population $x$ years after $2008$ . Round $m$ to two decimal places.

b. Use the model from part (a) to project the percentage of white non-Hispanics in the United States in $2108$.

Gotham City is trying to determine the type and location of recreational facilities to be built during the next decade. Four types of facilities are under consideration: golf courses, swimming pools, gymnasiams, and tennis courts. Six sites are under consideration. If a golf course is built, it must be built at either site 1 or site 6. Other facilities may be built at sites 2-5. The available land (in thousands of square feet) at each site is given in Table 64. The cost of building each facility (in thousands of dollars), the annual maintenance cost (in thousands of dollars) for each facility, and the land (in thousands of square feet) required for each facility are given in Table 65. The number of user days (in thousands) for each type of facility depends on where it is built. The dependence is given in Table 66. a. Consider the following set of priorities: Priority 1: Limit land use at each site to the land available. Priority 2: Construction costs should not exceed $1.2 million. Priority 3: User days should exceed 200,000. Priority 4: Annual maintenance costs should not exceed$200,000. For this set of priorities, use preemptive goal programming to determine the type and location of recreation facilities in Gotham City. b. Consider the following set of priorities: Priority 1: Limit land use at each site to the land available. Priority 2: User days should exceed 200,000. Priority 3: Construction costs should not exceed $1.2 million. Priority 4: Annual maintenance costs should not exceed$200,000. For this set of priorities, use preemptive goal programming to determine the type and location of recreation facilities in Gotham City. TABLE 64:

$$\begin{matrix} \text{ } & \text{Site}\\ \text{ } & \text{2} & \text{3} & \text{4} & \text{5}\\ \text{Land} & \text{70} & \text{80} & \text{95} & \text{120}\\ \end{matrix}$$

TABLE 65:

$$\begin{matrix} \text{Site} & \text{Construction Cost} & \text{Maintenance Cost} & \text{Land Required}\\ \text{Golf} & \text{340} & \text{80} & \text{Not relevant}\\ \text{Swimming} & \text{300} & \text{36} & \text{29}\\ \text{Gymnasium} & \text{840} & \text{50} & \text{38}\\ \text{Tennis courts} & \text{85} & \text{17} & \text{45}\\ \end{matrix}$$

TABLE 66:

$$\begin{matrix} \text{Site} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6}\\ \text{Golf} & \text{31} & \text{X} & \text{X} & \text{X} & \text{X} & \text{27}\\ \text{Swimming} & \text{X} & \text{25} & \text{21} & \text{32} & \text{32} & \text{X}\\ \text{Gymnasium} & \text{X} & \text{37} & \text{29} & \text{28} & \text{38} & \text{X}\\ \text{Tennis courts} & \text{X} & \text{20} & \text{23} & \text{22} & \text{20} & \text{X}\\ \end{matrix}$$

The United States has the most miles of roads in the world at about $4 \times 10^{6}$ miles. Japan has about $7.3 \times 10^{5}$ miles. How many more miles of roads does the United States have than Japan? Write in scientific notation.

In the tests with sodium iodide in acetone and silver nitrate in ethanol, why should $2$-bromobutane react faster than $2$-chlorobutane?