Assume that x2, x7 and x8 are the dollars invested in three different common stocks from the New York Stock Exchange. In order to diversify the investments, the investing company requires that no more than 52% of the dollars invested can be in "stock 2." If this constraint were written in standard form, what would be the coefficient for x2 (round to 2 decimal places)?
Question
Assume that x2, x7 and x8 are the dollars invested in three different common stocks from the New York Stock Exchange. In order to diversify the investments, the investing company requires that no more than 52% of the dollars invested can be in "stock 2." If this constraint were written in standard form, what would be the coefficient for x2 (round to 2 decimal places)?
Solution 1
The coefficient for x2 would be -0.52. This is because the constraint is that no more than 52% of the total investment can be in "stock 2". Therefore, if we write this constraint in standard form (i.e., less than or equal to), we would have -0.52x2 + x7 + x8 <= 0. This means that the investment in "stock 2" must be less than or equal to 52% of the total investment. Therefore, the coefficient for x2 is -0.52.
Solution 2
The coefficient for x2 would be -0.52. This is because the constraint is that no more than 52% of the total investment can be in "stock 2". Therefore, if we write this constraint in standard form (i.e., less than or equal to), we get -0.52x2 + x7 + x8 <= 0. This means that the investment in "stock 2" must be less than or equal to 52% of the total investment. Therefore, the coefficient for x2 is -0.52.
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