the snack shop makes 3 mixes of nuts in the following proportions.mix I: 6 lbs peanuts, 2 lbs cashews, 2 lbs pecans.Mix II: 5 lbs peanuts, 3 lbs cashews, 2 lbs pecans.Mix III: 3 lbs peanuts, 4 lbs cashews, 3 lbs pecans.they received an order for 25 of mix I, 18 of mix II, and 35 of mix III. write the matrices A & B for which AB gives the total number of lbs of each nut required to fill the order.
Accepted Solution
A:
Answer:[tex]A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}[/tex][tex]B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}[/tex]Step-by-step explanation:It is given that the snack shop makes 3 mixes of nuts in the following proportions.Mix I: 6 lbs peanuts, 2 lbs cashews, 2 lbs pecans.Mix II: 5 lbs peanuts, 3 lbs cashews, 2 lbs pecans.Mix III: 3 lbs peanuts, 4 lbs cashews, 3 lbs pecans.they received an order for 25 of mix I, 18 of mix II, and 35 of mix III.We need to find the matrices A & B for which AB gives the total number of lbs of each nut required to fill the order. Mix I Mix II Mix IIIpeanuts 6 5 3cashews 2 3 4pecans 2 2 2[tex]A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}[/tex][tex]B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}[/tex]The product of both matrices is[tex]AB=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}[/tex][tex]AB=\begin{bmatrix}6\cdot \:25+5\cdot \:18+3\cdot \:35\\ 2\cdot \:25+3\cdot \:18+4\cdot \:35\\ 2\cdot \:25+2\cdot \:18+3\cdot \:35\end{bmatrix}[/tex][tex]AB=\begin{bmatrix}345\\ 244\\ 191\end{bmatrix}[/tex]Therefore matrix AB gives the total number of lbs of each nut required to fill the order.