A tailor produces $x$ dresses and $y$ shirts during one week. Over that week, he produces at least 4 dresses, no more than 7 shirts, fewer than 14 dresses and shirts in total, and the number of shirts he produces is greater than $\frac{2}{3}$ of the number of dresses. One inequality that represents this information is $x \geq 4$.
(a)[3]
State the other three inequalities in $x$ and/or $y$.
(b)[6]
On the grid, plot 4 straight lines and shade the excluded regions to represent these inequalities. Label the region $R$ that satisfies all 4 inequalities.
(c)[1]
Use your diagram to determine the least number of dresses and the least number of shirts the tailor makes in one week.
(d)[2]
Use your diagram to determine the greatest profit the tailor can make in one week.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The inequalities are $y\leq7$, $x+y<14$, and $y>\frac23x$.” …