Business economics
When x thousand dollars are spent on labor and y thousand dollars on equipment, the output of a certain factory is Q(x,y) = 60×0.5y0.5. Suppose 200 thousand dollars is available for labor and equipment. Use Lagrange Multipliers to determine how the money should be allocated between labor and equipment to generate the largest output? Round to two decimal places if necessary and include units with your answer.
2. TV sets are produced in two factories A and B. Suppose “x” TV sets are produced at A and “y” TV sets are produced at B. The cost is given by C(x,y) =6×2+12y2. If you must produce 90 TV sets in total, what is the number of TV sets that should be produced in each factory in order to minimize the cost?
Refer to the following notes on linear regression and solve problem #3.
Linear regression_updated (1).pdf
3. The following table shows a country’s gross national product (GNP) for the period 1970-1973 (in millions of US dollars).
| Year | 1970 | 1971 | 1972 | 1973 |
| GNP | 79835 | 89112 | 97339 | 110156 |
Growth of GNP was almost exponential during the period. So, approximately:
GNP=Aea(t−t0),t0=1970
Define x = t – t0 and b = ln A. Then ln(GNP) = ax + b. On the basis of the table above, one gets the following
| Year | 1970 | 1971 | 1972 | 1973 |
| y=ln(GNP) | 11.29 | 11.40 | 11.49 | 11.61 |
Using the method introduced in the .pdf file (method of least squares), determine the straight line y = ax+b which best fits the data in the last table.
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