Exam 3: Marginal Analysis for Optimal Decision Making

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Fill in the blanks in the following table. Then use the table to answer the questions:X Fill in the blanks in the following table. Then use the table to answer the questions:X    -If X is decreased from 6 to 5 units, total benefit ___________ by $_________, and total cost ___________ by $_________. Thus, net benefit _____________. -If X is decreased from 6 to 5 units, total benefit ___________ by $_________, and total cost ___________ by $_________. Thus, net benefit _____________.

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decreases; 20; decreases; 75; increases

Use the following graph showing the marginal benefit and marginal cost curves for activity A to answer the following questions. Use the following graph showing the marginal benefit and marginal cost curves for activity A to answer the following questions.    -Net benefit is maximized when _________ units of A are chosen; marginal benefit is $_________ and marginal cost is $_________. -Net benefit is maximized when _________ units of A are chosen; marginal benefit is $_________ and marginal cost is $_________.

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200; $20; $20

refer to the following: 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: refer to the following: 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:     -If the manager currently hires four engineers and one market researcher, what must be true? -If the manager currently hires four engineers and one market researcher, what must be true?

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C

Use the following graph showing the marginal benefit and marginal cost curves for activity A to answer the following questions. Use the following graph showing the marginal benefit and marginal cost curves for activity A to answer the following questions.    -If 100 units of A are chosen, net benefit will increase by $_________ if one _________ unit of A is chosen. -If 100 units of A are chosen, net benefit will increase by $_________ if one _________ unit of A is chosen.

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refer to the following: The manager of the customer service department at a bank can hire employees with a high school degree (HS) who earn $10,000 annually or employees with a bachelor's degree (B) who earn $20,000. The manager wants to maximize the number of customers served given a fixed payroll. refer to the following: The manager of the customer service department at a bank can hire employees with a high school degree (HS) who earn $10,000 annually or employees with a bachelor's degree (B) who earn $20,000. The manager wants to maximize the number of customers served given a fixed payroll.    -If the manager currently has three HS and three B, what must be true? -If the manager currently has three HS and three B, what must be true?

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Fill in the blanks in the following table. Then use the table to answer the questions:X Fill in the blanks in the following table. Then use the table to answer the questions:X    -If activity X is increased from 3 to 4 units, total benefit ___________ by $_________. -If activity X is increased from 3 to 4 units, total benefit ___________ by $_________.

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Activity A has the following marginal (MB) and marginal cost (MC) functions: MB = 2,500 - 20A MC = 500 + 30A where MB and MC are measured in dollars. -The optimal level of the activity is ________ units. At the optimal level of activity, marginal benefit is $_________ and marginal cost is $__________. The total benefit (TB) and total cost (TC) functions for the activity are: TB = 2,500A -10A2 TC = 500A + 15A2 where TB and TC are measured in dollars.

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The marginal benefit and marginal cost functions for activity A are MB = 100 - 0.04A MC = 28 + 0.02A -The optimal level of A is _________ units at which MB = _________ and MC = ____________.

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Fill in the blanks in the following table. Then use the table to answer the questions:X Fill in the blanks in the following table. Then use the table to answer the questions:X    -The optimal level of activity is ___ units of activity X, and net benefit at the optimal level of X is $____________. -The optimal level of activity is ___ units of activity X, and net benefit at the optimal level of X is $____________.

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Use the following graph showing the marginal benefit and marginal cost curves for activity A to answer the following questions. Use the following graph showing the marginal benefit and marginal cost curves for activity A to answer the following questions.    -If 300 units of A are chosen, net benefit will increase by $_________ if one _________ unit of A is used. -If 300 units of A are chosen, net benefit will increase by $_________ if one _________ unit of A is used.

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The next questions refer to the following: A clinic uses doctors and nurses optimally and is servicing the maximum number of patients given a limited annual payroll. The last doctor hired treated 1,600 extra patients in a year, while the last nurse hired treated 1,000 extra patients in a year. -If doctors make $40,000 a year, what do nurses make?

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Activity A has the following marginal (MB) and marginal cost (MC) functions: MB = 2,500 - 20A MC = 500 + 30A where MB and MC are measured in dollars. -The 50th unit of the activity increases total benefit by $_________ and increases total cost by $_________. Since marginal benefit is _________ (greater, less) than marginal cost, subtracting the 50th unit of activity _________ (increases, decreases) net benefit by $_________.

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The marginal benefit and marginal cost functions for activity A are MB = 100 - 0.04A MC = 28 + 0.02A -The 800th unit of A increases total benefit by $_________ and total cost by $_________ thereby _____________________ net benefit by $__________.

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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. 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.    -With $550 to spend, the total number of units sold will be maximized by choosing ______ displays in grocery stores and ______ displays in convenience stores. With $550 to spend, the maximum number of units that can be sold is ________. -With $550 to spend, the total number of units sold will be maximized by choosing ______ displays in grocery stores and ______ displays in convenience stores. With $550 to spend, the maximum number of units that can be sold is ________.

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A decision maker can choose the levels of two activities, A and B, so as to maximize net benefits. The marginal benefit functions of A and B are A decision maker can choose the levels of two activities, A and B, so as to maximize net benefits. The marginal benefit functions of A and B are    Activity A costs $160 per unit and activity B Costs $540 per unit. -The optimal level of activity A is _________ units. Activity A costs $160 per unit and activity B Costs $540 per unit. -The optimal level of activity A is _________ units.

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refer to the following: 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 refer to the following: 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    -If the manager currently has two engineers and one market researcher, what must be true? -If the manager currently has two engineers and one market researcher, what must be true?

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In a constrained maximization problem with two activities, A and B, the highest level of benefits obtainable at a given level of cost is achieved when _______________ equals ____________ and the constraint is met.

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A decision maker can choose the levels of two activities, A and B, so as to maximize net benefits. The marginal benefit functions of A and B are A decision maker can choose the levels of two activities, A and B, so as to maximize net benefits. The marginal benefit functions of A and B are    Activity A costs $160 per unit and activity B Costs $540 per unit. -The optimal level of activity B is _________ units. Activity A costs $160 per unit and activity B Costs $540 per unit. -The optimal level of activity B is _________ units.

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Activity A has the following marginal (MB) and marginal cost (MC) functions: MB = 2,500 - 20A MC = 500 + 30A where MB and MC are measured in dollars. -For the optimal level of the activity in part c, the total benefit is $_________, the total cost is $_________, and the net benefit is $__________.

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A publishing house is using 400 printers and 200 printing presses to produce books. The printers' wage rate is $20 and the price of a printing press is $100. The last printer added 20 books to total output, while the last press added 50 books to total output. In order to maximize the number of books published with a budget of $28,000, the publishing house

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