Suppose the total cost of manufacturing q units of a certaincommodity is: C(q)=3q^2+5q+10

a) Derive a formula for the marginal cost.

b) Use the marginal cost to approximate the cost of producingthe 51st unit.

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Increase in capital investment : At a certain factory, the daily output is Q(K)=4000k^(1/2) units, where K denotes the firm's capital investment. Use calculus to estimate the percentage increase in output that will result from a 1 percent increase in capital investment. |

Derive a formula for the marginal cost : Suppose the total cost of manufacturing q units of a certaincommodity is: C(q)=3q^2+5q+10 |

Fuction of the number of units produced : A manufacturer's total cost consists of a fixed overhead of $200 plus production costs of $50 per unit. Expess the total cost as a fuction of the number of units produced. |

Determine the standard error of the proportion : There are 500 employees in a firm, 45% of whom are female. Asample of 60 employees is selected randomly. determine the standard error of the proportion. |

Examples of alternate hypothesis and rejection region : if the decision is to reject the null hypothesis of no difference between two population proportions , at the 5% level of significance , what are examples of the alternate hypothesis and rejection region ? |

Calculate the standard error of the mean : A simple random sample of 64 observations was taken from a large population. The population deviation is 120. The sample mean was determined to be 320. Calculate the standard error of the mean. |

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