Graphical solution of linear programs Quiz

1. The objective line $ax+by=k$ (with $a,b>0$) has gradient:

• A. $\frac{a}{b}$
• B. $-\frac{b}{a}$
• C. $-\frac{a}{b}$
• D. $\frac{b}{a}$

2. In the ruler method for a maximisation problem, the optimal point is:

• A. the first point of the region touched moving away from the origin
• B. the last point of the region touched moving away from the origin
• C. the point on the $x$-axis
• D. the origin

3. How are the exact coordinates of a vertex found?

• A. By solving the equations of the two boundary lines that meet there
• B. By substituting into the objective function
• C. By rounding values read from the graph
• D. By dividing the constraints

4. A region has vertices $(0,0)$, $(0,6)$, $(3,4)$ and $(5,0)$. What is the maximum of $P=3x+2y$?

• A. 12
• B. 15
• C. 17
• D. 18

5. The non-integer optimum of a problem is at $(3.75,\,7.5)$. Why is $(4,8)$ not necessarily the integer solution?

• A. Integers are always smaller
• B. Rounding up always gives the optimum
• C. It has the wrong gradient
• D. It may lie outside the feasible region