Graphical solution of linear programs Quiz

1. What is the gradient of the objective line $3x+4y=k$?

• A. $\frac34$
• B. $-\frac34$
• C. $-\frac43$
• D. $\frac43$

2. A feasible region has vertices $(0,0)$, $(5,0)$, $(3,4)$ and $(0,6)$. The objective $2x+y$ is maximised. Which is correct?

• A. Only $(5,0)$ is optimal
• B. Only $(3,4)$ is optimal
• C. Every point on the edge from $(5,0)$ to $(3,4)$ is optimal
• D. $(0,6)$ is optimal

3. Why can rounding the optimal vertex be wrong for an integer problem?

• A. The rounded point may be infeasible or not optimal
• B. Rounding always gives a better answer
• C. Integer problems have no feasible region
• D. Vertices are never optimal

4. Minimise $C=2x+y$ with vertices $(7,1)$, $(4,2)$ and $(2,5)$. Which vertex is optimal?

• A. $(7,1)$
• B. $(4,2)$
• C. All equal
• D. $(2,5)$

5. The LP maximum of $P=3x+2y$ is $19.5$. For whole-number $x,y$, the maximum possible $P$ is at most

• A. $19.5$
• B. $20$
• C. $19$
• D. $18$