Mathematics 4024 · O Level · Algebraic manipulation

Algebraic manipulation — practice question

Anya manufactures T-shirts. Matrix $M$ displays how many T-shirts of each type she makes in one week.
(a)[1]

Anya sells every one of these T-shirts to a shop. She asks $\$5$ for each small T-shirt, $\$6$ for each medium T-shirt and $\$8$ for each large T-shirt. Show these prices in a $3 \times 1$ column matrix $N$.

(b(i))[2]

Calculate $P = MN$.

(b(ii))[1]

Explain what the entries of matrix $P$ stand for.

(c(i))[2]

The shopkeeper charges $\$10$ for every men’s T-shirt and $\$9.50$ for every women’s T-shirt. Calculate $(10\;\;9.50)\begin{pmatrix}10&25&30\\20&40&25\end{pmatrix}.

(c(ii))[3]

Work out the percentage profit the shopkeeper makes when all of the T-shirts are sold.

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