Karen Sandberg, your competition in Suburban State U's T-shirt market, has apparently been undercutting your prices and outperforming you in sales. Last week she sold 120 tie-dyed shirts for $12 each, 80 (low quality) crew shirts at $1 apiece, and 50 lacrosse T-shirts for $6 each. Use matrix operations to calculate her total revenue for the week.

Question

Karen Sandberg, your competition in Suburban State U's T-shirt market, has apparently been undercutting your prices and outperforming you in sales. Last week she sold 120 tie-dyed shirts for $12 each, 80 (low quality) crew shirts at $1 apiece, and 50 lacrosse T-shirts for $6 each. Use matrix operations to calculate her total revenue for the week. ​

Quizplus · Accepted Answer

To calculate Karen's revenue, we need to multiply the number of shirts sold by their respective prices and then add up the products.

Let x be the matrix of the number of shirts sold, and y be the matrix of the prices:

x = \begin{pmatrix} 120 & 80 & 50 \end{pmatrix}

y = \begin{pmatrix} 12 \ 1 \ 6 \end{pmatrix}

The product of x and y gives us the total revenue:

xy = \begin{pmatrix} 120 & 80 & 50 \end{pmatrix} \begin{pmatrix} 12 \ 1 \ 6 \end{pmatrix} = (120 \cdot 12) + (80 \cdot 1) + (50 \cdot 6) = 1,820

Therefore, Karen's total revenue for the week was $1,820, which is option C.

Karen Sandberg, Your Competition in Suburban State U's T-Shirt Market