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Thus we have two equations for the two unknowns, x and z. Solving these equations gives us x* = 0.2887 and z* = 4.3923, which is the amount that the Government needs to contribute to bring back profit to the original level.
Figure 1. The profit functions for the three optimization scenarios represented in the figure…

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The horizontal dotted line indicates that the blue curve and the green curve have the same maximum. The vertical dotted lines indicate the maxima for the three curves, respectively.
g) The weight of the heads of household appears to be normally distributed. Wages however are extremely skewed, resulting in many households with low wages and a few with high wages. The education level is a symmetric, discrete distribution, with both highly educated and less educated heads of households being rare. Since weight is the only symmetric distributed variable in the table, only in its case are the sample mean and median close to each other. Another indication that weight is indeed normally distributed is the proximity of the actual percentages of weights falling within the three given intervals to the empirical percentages. This is because the empirical percentages are calculated assuming normality of the data. An interesting observation is that the size of the 95% confidence interval for clothing and recreational expenses is actually much higher than that of more basic expenses such as food and housing. It is also interesting to note that clothing and recreational expenses are more tightly correlated with net income than food and household expense are, as indicated by the marginally higher correlation coefficient of TOTEXP2 with FINC than TOTEXP1 with FINC. ...
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