dolution

dolution.

An ongoing policy debate concerns whether to legalize the use of drugs such as marijuana and cocaine. Some researchers estimate that legalizing cocaine would cause its price to fall by as much as 95 percent. Proponents of legalization argue that legalizing drug use would lower crime rates by eliminating the main reason for the murderous gang wars that plague many big cities and by reducing the incentive for drug addicts to commit robberies and burglaries. Opponents of legalization argue that lower drug prices would lead more people to use drugs.14$11.44$10.478.148.01$11.47a)Suppose the price elasticity of demand for cocaine is -2. If legalization causes the price of cocaine to fall by 95 percent, what will be the percentage increase in the quantity of cocaine demanded?EpDemand = % change Qd or , 2 = % change Qd= 190% change P95The percentage increase in the quantity demanded for cocaine would be 190%. In this scenario, you know that the price elasticity of demand for cocaine is elastic because of its coefficient of 2.You are asked to calculate the % change in quantity demanded knowing the other two variables (elasticity and % change in price). A 95% decrease in the price of cocaine would then lead to an increase in the quantity demanded for cocaine of 190%. b)If the price elasticity is -0.02, what will be the percentage increase in the quantity demanded?EpDemand = % change Qd or , .02 = % change Qd= 1.90% change P95Clearly, the higher the absolute value of the price elasticity of demand for cocaine, the greater the increase in cocaine use that would result from legalization. If the price elasticity is as high as in question A, legalization will lead to a large increase in use. If, however, the price elasticity is as low as in question B, legalization will lead to only a small increase in use. 36. In summer 2007, Sony decided to cut the price of its Playstation 3 video game console from $600 to $500. One industry analyst forecast that the price cut would increase sales from 80,000 units per monthto 120,000 units per month. Assuming the analystâs forecast is correct, calculate the price elasticity of demand for Playstation 3.$500 / $600 -1 = 17% cut in price; 120,000 / 80,000 = 50% increase in salesEpDemand = % change Qd or , = 50%= 2.94% change P17%The coefficient for the price elasticity of demand is 2.94, meaning that the cut in price of Playstation 3 is very elastic as is also evidenced by the 50% increase in quantity demanded from a lesser percentage decrease in the price of the video game console.

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Consider The Following Mixed-Integer Linear Program: Max 2×1 + 3.9 S.T. 4×4 + 9×2 = 36 7x + 3xy S 35 ** 20

X integer a. Graph the constraints for this problem. Indicate on your graph all feasible mixed- integer solutions. h. Find the optimal solution to the LP Relaxation. Round the value of x down to find a feasible mixed-integer solution. Is this solution optimal? Why or why not? c. Find the optimal solution for the mixed-integer linear program. 2- Grave City is considering the relocation of several police substations to obtain better en forcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table: Potential Locations for Substations

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Natalie,

her husband, her son, and four additional friends are

driving in two vehicles to the seashore. (a) If all seven people can drive, how many ways can

the two drivers be selected? (Everyone wants to

drive the sports car, so it is important which driver

gets which car.)

(b) If the sports car must be driven by Natalie, her

husband, or their son, how many ways can the

drivers now be determined?

(c) If the sports car will accommodate only two people,

and there are no other restrictions, how many

ways can both drivers and passengers be assigned

to both cars?

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Soil Testing A researcher took water samples from a stream running through a forest and groundwater in the forest. The samples were collected over the course of a year. Each sample was analyzed for the concentration of dissolved organic carbon (mg/L) in it and categorized according to the type of water collected. Water was collected from streams (surface water), groundwater was collected from organic soil, and groundwater was collected from mineral soil. The researcher wanted to determine if the mean concentration of dissolved organic carbon was the same for each collection area. The results are presented in the following table.

(a) What is the response variable in this study?

(b) What is the factor? How many levels of treatment does the factor have?

(c) State the null and alternative hypotheses.

(d) A normal probability plot of each sample (organic, mineral, and surface) indicates the data come from a normally distributed population. Use the following summary statistics from StatCrunch to verify the equal population standard deviation requirement.

(e) Use the following StatCrunch output to test if the means are the same at the  level of significance.

(f) Interpret the -value.

(g) Shown are side-by-side boxplots of each type of collection area drawn in StatCrunch. Do the boxplots support the analytic results? Which collection area type appears to differ from the rest?

(h) The following display represents the results of Tukey’s test obtained from StatCrunch. Which pairwise means differ?

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