Olé Oil produces three products heating oil, gasoline, and jet fuel. The average octane levels must be at least 4.5 for heating oil, 8.5 for gas, and 7.0 for jet fuel. To produce these products Olé purchases two types of oil: crude 1 (at $12 per barrel) and crude 2 (at$10 per barrel). Each day, at most 10,000 barrels of each type of oil can be purchased. Before crude can be used to produce products for sale, it must be distilled. Each day, at most 15,000 barrels of oil can be distilled. It costs 10¢ to distill a barrel of oil. The result of distillation is as follows: (1) Each barrel of crude 1 yields 0.6 barrel of naphtha, 0.3 barrel of distilled 1, and 0.1 barrel of distilled 2. (2) Each barrel of crude 2 yields 0.4 barrel of naphtha, 0.2 barrel of distilled 1, and 0.4 barrel of distilled 2. Distilled naphtha can be used only to produce gasoline or jet fuel. Distilled oil can be used to produce heating oil or it can be sent through the catalytic cracker (at a cost of 15¢ per barrel). Each day, at most 5,000 barrels of distilled oil can be sent through the cracker. Each barrel of distilled 1 sent through the cracker yields 0.8 barrel of cracked 1 and 0.2 barrel of cracked 2. Each barrel of distilled 2 sent through the cracker yields 0.7 barrel of cracked 1 and 0.3 barrel of cracked 2. Cracked oil can be used to produce gasoline and jet fuel but not to produce heating oil. The octane level of each type of oil is as follows: naphtha, 8; distilled 1, 4; distilled 2, 5; cracked 1, 9; cracked 2, 6. All heating oil produced can be sold at $14 per barrel; all gasoline produced.$18 per barrel; and all jet fuel produced, $16 per barrel. Marketing considerations dictate that at least 3,000 barrels of each product must be produced daily. Formulate an LP to maximize Olé’s daily profit.

_____ saclike pocket with highly folded walls for respiration.

The mayor of Llanview is trying to determine the number of judges needed to handle the judicial caseload. Table 84:

$$\begin{matrix} \text{Month} & \text{Hours}\\ \text{January} & \text{400}\\ \text{February} & \text{300}\\ \text{March} & \text{200}\\ \text{April} & \text{600}\\ \text{May} & \text{800}\\ \text{June} & \text{300}\\ \text{July} & \text{200}\\ \text{August} & \text{400}\\ \text{September} & \text{300}\\ \text{October} & \text{200}\\ \text{November} & \text{100}\\ \text{December} & \text{300}\\ \end{matrix}$$

During each month of the year it is estimated that the number of judicial hours needed is as given in Table 84. a. Each judge works all 12 months and can handle as many as 120 hours per month of casework. To avoid creating a backlog, all cases must be handled by the end of December. Formulate an LP whose solution will determine how many judges Llanview needs. b. If each judge received one month of vacation each year, how would year answer change?

Sketch a graph of the function and completely discuss the graph. $f(x)=\frac{4}{x^{2}-1}$

The Gotham City Police Department employs 30 police officers. Each officer works 5 days per week. The crime rate fluctuates with the day of the week, so the number of police officers required each day depends on which day of the week it is: Saturday, 28; Sunday, 18; Monday, 18; Tuesday, 24. Wednesday, 25. Thursday, 16; Friday, 21. The police department wants to schedule police officers 10 minimize the number whose days off are not consecutive Formulate an LP that will accomplish this goal. (Hint Have a constraint for each day of the week that ensures that the proper number of officers are not working on the given day.)

Consider the emission spectrum of singly ionized helium $\left( \mathrm { He } ^ { + } \right)$. Find the longest three wavelengths for the series in which the electron makes a transition from a higher excited state to the first excited state (not the ground state).

Finco has the following investments available. Investment A: For each dollar invested at time 0. we receive $0.10 at time 1 and$1.30 at time 2. (Time 0 = now, time 1 = one year from now; and so on.) Investment B: For each dollar invested at time 1, we receive $1.60 at time 2. Investment C: For each dollar invested at time 2, we receive$1.20 at time 3. At any time, leftover cash may be invested in T-bills, which pay 10% per year. At time 0, we have $100. At most,$50 can be invested in each of investments A, B, and C. Formulate an LP that can be used to maximize Finco’s cash on hand at time 3.

What is bioluminescence and what do midwater animals use it for?

If 100. g of water at $80^{\circ} \mathrm{C}$ contains 45 g of KC1 and 45 g of $\mathrm{NaNO}_{3}$, the solution is (1) saturated with respect to both KCl and $\mathrm{NaNO}_{3}$ (2) saturated with respect to KCl and unsaturated with respect to $\mathrm{NaNO}_{3}$ (3) unsaturated with respect to both KCl and $\mathrm{NaNO}_{3}$ (4) supersaturated with respect to both KCl and $\mathrm{NaNO}_{3}$

Jake has $25,000 worth of property damage insurance and$1,000-deductibIe collision insurance. He caused an accident that damaged a $2,000 sign, and he also did$2,400 worth of damage to another car. His car had $2,980 worth of damage done. a. How much will the insurance company pay under Jake's property damage insurance? b. How much will the insurance company pay under Jake's collision insurance? c. How much of the damage must Jake pay for?

Use the given information to write the equation of the parabola. vertex: (0, 0); directrix: x = -3

Use the difference of squares to factor each binomial over the set of real numbers. a. $x^{2} - 64$ b. $x^{4} - 16$ c. $x^{8} - 1$ d. $x^{4} - y^{4}$

In keeping with the theme of the restaurant, the customer wants to include tables in the shapes of triangles, parallelograms, and trapezoids. Lisa decides to investigate area formulas by first finding the formula for the area of a parallelogram. Use appropriate tools strategically. Pick a point, not a vertex, on one side of the rectangle. Draw a segment from the point to a vertex on the opposite side of the rectangle. Cut along the segment. Put the two figures together to form a parallelogram. Explain why the area of a parallelogram is the same as the area of rectangle. Nelson and Rashid, two tabletop designers, are discussing how to calculate the area of any parallelogram. Nelson suggests that they multiply the lengths of two consecutive sides to find the area, as they do for rectangles. Rashid claims this will not work. Explain which designer is correct and why.

Find the regression equation, letting the first variable be the predictor (x) variable. Using the bill / tip data, find the best predicted tip amount for a dinner bill of $100. What tipping rule does the regression eq uation suggest?

$$\begin{array} { |c| c | c | c | c | c | c | } \hline \text{Bill (dollars)}&33.48 & { 50.68 } & { 87.92 } & { 98.84 } & { 63.60 } & { 107.34 } \\ \hline \text{Tip (dollars)}&5.50 & { 5.00 } & { 8.08 } & { 17.00 } & { 12.00 } & { 16.00 } \\ \hline \end{array}$$