[填空题]
John operates a small clothing : (kjdkqjd8w(cj2b q9y3 ,cy/ k8q bnwfactory that manufactures jeans. John observes tyzg(i(4p4 ghzhatz y(g4pzg(hi 4 the weekly total production cost, C , in Australian dollars (AUD), and the number of jeans produced per week, N , can be related by the equation
$C=a N^{b}+K$,
where a, b and K are positive constants.
John estimates that the weekly total fixed cost of operating the factory is 7500 AUD.
1. Write down the value of K .
After analysing the financial accounting records of a particular month, John finds the data given below.
2. Draw a scatter diagram of $\ln (C-K)$ versus $\ln N$ , scaling and shifting the axes if needed.
3. State the type of model that best fits the data displayed on your scatter diagram from part (b).
4. Write down the equation of the regression line of $\ln (C-K) $ on $\ln N$ .
5. Hence find the value of a and the value of b .
John wants to increase the production rate of jeans up to 1000 pairs per week. a = b =
6. Using John's equation, estimate the weekly total cost of producing 1000 jeans. ≈ AUD
7. State whether it is valid to use John's equation to estimate the weekly total cost of producing 1000 jeans. Give a reason for your answer.
8. 1. Describe how the data must be entered into your G.D.C. to determine John's equation using power regression method.
2. Hence verify your answers to part (e). a = b =
