Karen Morrison and Nick Hamshaw Solutions for Exercise 7: Exercise 14.7

In the diagram, the unshaded region represents the set of inequalities $x⩽6$, $0⩽y⩽6$ and $x+y⩾4$. Find the greatest and least possible values of $3x+2y$ subject to these inequalities.

On a grid, shade the unwanted regions to indicate the region satisfying all the inequalities $y⩽x, x+y⩽6$ and $y⩾0$

In the diagram the unshaded region represents the set of inequalities $x+2y⩾6$, $y⩽x$ and $x<4$. Find the greatest possible value of $2x+y$ if $x$ and $y$satisfies all these inequalities?

The whole numbers $x$ and $y$ satisfy all the inequalities $y⩾1$, $y⩽x+3$ and $3x+y⩽6$. find the greatest and least possible values of the expression $x+y$

An IGCSE class is making school flags and T-shirts to sell to raise funds for the school. Due to time constraints, the class is able to make at most $150$ flags and $120$ T-shirts. The fabric is donated and they have enough to make $200$ items in total. A flag sells for $\$2$ and T-shirt sells for $\$5$. How many of each item should they make to maximize their income from sales?

A school principal wants to buy some book cases for the school library. She can choose two types of book case. Type A costs $\$10$ and it requires $0.6 {\mathrm{m}}^2$ of floor space and holds $0.8 {\mathrm{m}}^3$ of books. Type B costs $\$20$ and it requires $0.8 {\mathrm{m}}^2$ of floor space and holds $1.2 {\mathrm{m}}^3$ of books. The maximum floor space available is $7.2 {\mathrm{m}}^3$ and the budget is $\$140$(But the school would prefer to spend less). What number and type of book cases should the principal buy to get the largest possible storage space for books?