Exam 3: Marginal Analysis for Optimal Decisions

In order to minimize the NET costs associated with crime,

A student taking economics,statistics,and finance has decided to spend 9 hours per week studying.The objective is to maximize the average grade,which means maximizing the total grade in the three courses.The table shows the student's estimate of the relation between time spent studying each course and the grade for each course. Based on the above information,what is the maximum AVERAGE grade the student can earn if she studies 9 hours per week?

A restaurant hires cooks and waiters.Cooks earn $10 an hour; waiters earn $5 an hour.The manager,who wants to maximize the number of meals served given a fixed payroll of $45 per hour,expects the following from cooks and waiters: $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Total wumber of meals seived }$ Number of employees 1 2 3 4 5 Cook 200 380 540 660 740 Waiter's 120 230 310 360 390 Given the above information,at the optimal choice,the last dollar spent on hiring waiters yielded

Refer to the figure below,which shows marginal benefits (MB)and marginal cost (MC)of activity A: If the decision maker is choosing 200 units of activity A,

A clinic uses doctors and nurses to serve the maximum number of patients given a limited annual payroll.The clinic currently has 10 doctors and 30 nurses.The last doctor hired can serve 300 additional patients,while the last nurse hired can serve 200 additional patients.If doctors make $60,000 a year and nurses make $20,000 a year,the clinic

A manager in charge of new product development can hire engineers and market researchers.The annual salary of an engineer is $40,000,while a market researcher receives $20,000.The marginal contributions of engineers and market researchers are: Based on the above information,if the manager currently hires four engineers and one market researcher,what must be true?

Gonzo consumes only two things--coke and hot dogs.We can define the addition to "happiness" of consuming an additional coke as the marginal utility of coke and that for hot dogs as the marginal utility of hot dogs.The prices of coke and hot dogs are fixed and Gonzo has a limited budget.To maximize "happiness" subject to his limited budget,Gonzo should purchase coke and hot dogs so that

If profits depend on both how much is produced (output)and on the level of advertising,then a profit-maximizing firm should choose the levels of output and advertising at which

A computer services center has a problem with "malicious" computer usage.The center's director has decided to hire additional personnel to monitor computer usage.In order to maximize the net benefit from hiring monitors,the director should hire the number of monitors at which

A local charity has decided to solicit donations door-to-door.The table below shows estimated donations for each hour a volunteer spends in the city,in the suburbs,and on campus. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Total Donations fiom: }$ Number of Hours The city The suburbs Campus 1 \ 75 \ 65 \ 45 2 147 127 87 3 215 185 125 4 279 239 159 5 337 289 189 6 380 333 209 Given the above information,with 10 hours of soliciting,the maximum possible amount of donations is

The optimal level of pollution reduction is that level at which

A politician,who wants to receive the maximum number of votes,spends 9 hours a week speaking to various groups.The table below shows his estimates of how time spent with each group will affect the number of votes he receives: Based on the information above,how should the politician allocate his speaking time?

A housecleaning company receives $25 for each house cleaned.The table below gives the relation between the number of workers and the number of houses that can be cleaned per week. Momber of Wariters Hauses Cieaved 1 9 2 17 3 24 4 30 5 35 Based on the above info,if the wage rate of a housecleaner is $130,what is the maximum amount of profit the company can earn?

Dr.X,an assistant professor at a large state university,is trying to decide how to allocate the 50 hours a week she spends working among the various activities expected of an assistant professor.The professor wants to maximize her raise next year and the table shows estimates of how time spent in each activity will contribute to her raise: Given the above information,if she decides that she will work 54 hours a week instead,how should she allocate her time?

A grocery store hires cashiers and baggers.Cashiers earn $8 an hour; baggers earn $4 an hour.The manager,who wants to maximize the number of customers served given a fixed payroll,expects the following productivity from cashiers and baggers: Tgtal number of customars served Number af employees Cashiers Baggers 1 240 136 2 440 264 3 600 384 4 712 496 5 776 560 Given the above information,with a payroll of $32 (per hour),how should the manager allocate this budget?

an unconstrained maximization problem

A local charity has decided to solicit donations door-to-door.The table below shows estimated donations for each hour a volunteer spends in the city,in the suburbs,and on campus. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Total Donations fiom: }$ Number of Hours The city The suburbs Campus 1 \ 75 \ 65 \ 45 2 147 127 87 3 215 185 125 4 279 239 159 5 337 289 189 6 380 333 209 Given the above information,how should a volunteer allocate 10 hours in order to maximize the amount of total donations?

A local charity has decided to solicit donations door-to-door.The table below shows estimated donations for each hour a volunteer spends in the city,in the suburbs,and on campus. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Total Donations fiom: }$ Number of Hours The city The suburbs Campus 1 \ 75 \ 65 \ 45 2 147 127 87 3 215 185 125 4 279 239 159 5 337 289 189 6 380 333 209 Given the above information,and given an optimizing solution,the fourth hour solicited yielded

Randolph is taking three courses this semester: economics,statistics,and finance.He has decided to spend 20 hours per week studying (in addition to attending all his classes)and his objective is to maximize his average grade,which means maximizing the total of his grades in the three courses.The table shows Randolph's estimate of the relation between time spend studying and his grade for each course. Based on the above info,how should Randolph allocate his time?

Your firm sells club soda in both grocery stores and convenience stores.You have a budget of $550 for store displays and must decide how to allocate this budget between grocery stores and convenience stores to maximize the total number of sales.The following table shows the total number of units that can be sold in grocery stores and convenience stores,according to the number of displays in each type of store.Displays in grocery stores cost $150 each and displays in convenience stores cost $100 each. Given the above information,at the optimal choice with a budget of $550,the last dollar spent on grocery store displays yields