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QUESTION $2$

A publishing company produces two mathematics textbooks. A copy of textbook A costs R$30$ to print and R$50$ to bind, whereas a copy of textbook $B$ costs R$40$ to print and R$20$ to bind. The company's budget allows for at most R$10000$ to be spent on printing and at most R$18200$ on binding. The profit derived from book $A$ is R$50$ per copy and from book $B$ is R$70$ per copy.

$2\mathrm{.}1($a$)$ Express the production problem in terms of a system of constraint inequalities.

$($b$)$ Give an objective function for the total profit.

$(2)$

$2\mathrm{.}2$ Sketch the feasible region for this production process.

$2\mathrm{.}3$ Determine the number of books A and $B$ that should be produced to maximise the profit.

$(4)$

$[17]$