An investment company sells 3 types of pooled funds, Standar

Linear spaces and subspaces, linear transformations, bases, etc.
king&i
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Joined: Sat Mar 07, 2009 5:13 pm

An investment company sells 3 types of pooled funds, Standar

An investment company sells 3 types of pooled funds, Standard (S), Deluxe (D), and Gold (G). Each unit of S contains 12 shares of stock A, 16 of Stock B, and 8 of Stock C. Each unit of D contains 20 shares of Stock A, 12 shares of stock B and 28 of Stock C. Each unit of G contains 32 shares of A, 28 of B and 36 of Stock C.

Suppose an investor wishes to purchase exactly 220 shares of Stock A, 176 shres of stock B and 264 sharss of Stock C by buying units of the 3 funds. Determine those combinations of units of S,D and G which will meet the investors requirements exactly.

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stapel_eliz
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An investment company sells 3 types of pooled funds, Standard (S), Deluxe (D), and Gold (G). Each unit of S contains 12 shares of stock A, 16 of Stock B, and 8 of Stock C. Each unit of D contains 20 shares of Stock A, 12 shares of stock B and 28 of Stock C. Each unit of G contains 32 shares of A, 28 of B and 36 of Stock C.

Suppose an investor wishes to purchase exactly 220 shares of Stock A, 176 shres of stock B and 264 sharss of Stock C by buying units of the 3 funds. Determine those combinations of units of S,D and G which will meet the investors requirements exactly.
Set this up as a system of linear equations, using variables to stand for the numbers of units of each type of pooled fund.

. . . . .stock A: 12s + 20d + 32g = 220
. . . . .stock B: 16s + 12d + 38g = 176
. . . . .stock C: 8s + 28d + 36g = 264

Solve the system for the values of "s", "d", and "g".