# Science:Math Exam Resources/Courses/MATH152/April 2011/Question B 01 (a)

MATH152 April 2011
Other MATH152 Exams

### Question B 01 (a)

Three identical fields of size one hectare are planted with different amounts of three kinds of wheat (types 1, 2 and 3). The first field is divided in three equal parts with one type of wheat planted on each part. It yields 12 tons of total harvest. The second field is divided in two equal parts with type 2 planted on one part and type 3 planted on the other. It yields 10 tons. The third field is divided in two equal parts with type 1 planted on one part and type 2 on the other. It yields 16 tons.

Let

$\mathbf {x} ={\begin{bmatrix}x_{1}\\x_{2}\\x_{3}\end{bmatrix}}$ be the vector of unknowns, where $x_{k}$ is the yield in tons per hectare of wheat type k. Describe the information above as as a linear system in the form

$A\mathbf {x} =\mathbf {b}$ (write A and b with specific values).

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