Economics: Marginal Benefits and Costs The table gives the marginal benefit and marginal cost of producing x units of a product for a given company. (a) Plot the points in each column and use the regression feature of a graphing utility to find a linear model for marginal benefit and a quadratic model for marginal cost as functions of the units produced x . (b) Use integration to find the benefit B and cost C equations. Assume B (0) = 0 and C (0) = 425. ( c ) Find the intervals in which the benefit exceeds the cost of producing x units. Make a recommendation for how many units the company should produce based on your findings. (Source: Adapted from Taylor, Economics, Fifth Edition) Number of units 1 2 3 4 5 Marginal benefit 330 320 290 270 250 Marginal cost 150 120 100 110 120 Number of units 6 7 8 9 10 Marginal benefit 230 210 190 170 160 Marginal cost 140 160 190 250 320 Spreadsheet at LarsonAppliedCalculus.com
Economics: Marginal Benefits and Costs The table gives the marginal benefit and marginal cost of producing x units of a product for a given company. (a) Plot the points in each column and use the regression feature of a graphing utility to find a linear model for marginal benefit and a quadratic model for marginal cost as functions of the units produced x . (b) Use integration to find the benefit B and cost C equations. Assume B (0) = 0 and C (0) = 425. ( c ) Find the intervals in which the benefit exceeds the cost of producing x units. Make a recommendation for how many units the company should produce based on your findings. (Source: Adapted from Taylor, Economics, Fifth Edition) Number of units 1 2 3 4 5 Marginal benefit 330 320 290 270 250 Marginal cost 150 120 100 110 120 Number of units 6 7 8 9 10 Marginal benefit 230 210 190 170 160 Marginal cost 140 160 190 250 320 Spreadsheet at LarsonAppliedCalculus.com
Solution Summary: The author explains how to use ti- 83 graphing calculator to find the function that best fits the data.
Economics: Marginal Benefits and Costs The table gives the marginal benefit and marginal cost of producing x units of a product for a given company. (a) Plot the points in each column and use the regression feature of a graphing utility to find a linear model for marginal benefit and a quadratic model for marginal cost as functions of the units produced x. (b) Use integration to find the benefit B and cost C equations. Assume B(0) = 0 and C(0) = 425. (c) Find the intervals in which the benefit exceeds the cost of producing x units. Make a recommendation for how many units the company should produce based on your findings. (Source: Adapted from Taylor, Economics, Fifth Edition)
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