Exam 3: Marginal Analysis for Optimal Decision Making

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,and given a budget of $550,the maximum possible number of sales is

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 many EXTRA votes will the politician receive if he devotes one more hour to speaking engagements i.e.,speaks 10 instead of 9 hours per week)?

Refer to the following table: What is the marginal cost of the 1^st unit of the activity?

Whenever the additional revenue from the last unit of output exceeds the additional cost of that unit,a profit-maximizing firm should

a constrained minimization problem,the decision maker

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?

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 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

Gigi consumes only Perrier and cheese.In order to maximize her happiness subject to limited income,Gigi should purchase the amounts of Perrier and cheese at which

A toy manufacturer is experiencing quality problems on its assembly line.Every defective toy that leaves the factory costs the firm $20.The firm has decided to hire quality inspectors to catch defective toys before they leave the factory. Given the above information,if the cost of each defective toy rises to $50,while inspectors are paid $150 a day,how many inspectors should the firm hire?

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: Given the above information,the manager should hire

A manager in charge of new product development can hire engineers and market researchers.The annual salary of an engineer is $30,000 and that of a market researcher is $20,000.The marginal contribution of engineers and market researchers are Given the above information,if the manager currently has two engineers and one market researcher,what must be true?

A restaurant currently has two cooks and ten waiters.Cooks earn $10 an hour and waiters earn $5 an hour.The last cook added 40 meals served to total output,while the last waiter added 25 meals served to total output.In order to maximize the number of meals served with a fixed budget,the manager should

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 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,how should the student allocate her time?

Refer to the following table: The optimal level of activity is:

Use the following marginal benefit and marginal cost functions for activity A: MB = 100 - 5A MC = 20 + 3A The optimal level of A is

Refer to the following table: What is the marginal cost for the 5th unit of the activity?

A Blue Ribbon Committee has decided that acid rain should be reduced and is trying to determine the optimal level of reduction.There are benefits from reducing acid rain more wildlife and forests,better health,etc.),but there are also costs.The committee estimates that the marginal benefit of each unit of reduction is $1,400 -5R,where R is units of reduction,and the marginal cost is 2R.If the committee wants to maximize the net benefit from reducing acid rain,what is marginal cost at the optimal level of reduction?

A firm can maximize profit net benefit)by choosing to produce that level of output at which