Answer to Question #124247 in Linear Algebra for adu frederick

Question

Popostino`s company has two pizza shops namely, Yesu Nkoaa and Yesu Nti at Assin Fosu and Winneba respectively. the number of Pacific Veggie, Pepperoni and Buffalo Chicken and large pizzas sold the last two weeks at at the two pizzerias is shown in the table below
Pizzerias Paccific Veggie Pepperoni Bufffalo Chicken
Yesu Nkoaa 350 504 413
Yesu Nti 248 622 512
The selling price for each pizzas is shown in the table below
Paccific Veggie Pepperoni Bufffalo Chicken
price $15.99 $23.99 $17.99

a. Write down a matrix multiplication that finds the total amount of income from sales of the three types of pizzas that each pizzeria generated during last two weeks.
b. Hence find the total amount of income from sales of the three types of pizzas that each pizzeria generated during last two weeks. Give your Answers correct to two decimal places.

Answer 1

Solution.

a.$\begin{pmatrix} 350 & 504 & 413\\ 248 & 622 & 512 \end{pmatrix} \begin{pmatrix} 15.99 \\ 23.99\\ 17.99 \end{pmatrix}= \begin{pmatrix} 25117.33 \\ 28098.18 \end{pmatrix};$

$A_{1,1}=350\sdot15.99+504\sdot23.99+413\sdot17.99=25117.33;$

$A_{2,1}=248\sdot15.99+622\sdot23.99+512\sdot17.99=28098.18;$

b. Pizzerias Paccific Veggie received income for two weeks 25117.33$;

Pepperoni Bufffalo Chicken  received income for two weeks 28098.18$;

Answer: a. $\begin{pmatrix} 25117.33 \\ 28098.18 \end{pmatrix};$

b. Pizzerias Paccific Veggie received income for two weeks 25117.33$;

Pepperoni Bufffalo Chicken  received income for two weeks 28098.18$.