solve for the number of large and small boxes sent out last week.
Added by Mar P.
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The given information is that a total of 100 boxes were sent out last week. Show more…
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The Bread Box, a small neighborhood bakery, sells four main items: sweet rolls, bread, cakes, and pies. The amount of each ingredient (in cups, except for eggs) required for these items is given by matrix A. $$ \left[\begin{array}{ccccc} 1 & 4 & \frac{1}{4} & \frac{1}{4} & 1 \\ 0 & 3 & 0 & \frac{1}{4} & 0 \\ 4 & 3 & 2 & 1 & 1 \\ 0 & 1 & 0 & \frac{1}{3} & 0 \end{array}\right]=A $$ The cost (in cents) for each ingredient when purchased in large lots or small lots is given by matrix $B$ $$ \left[\begin{array}{rr} 5 & 5 \\ 8 & 10 \\ 10 & 12 \\ 12 & 15 \\ 5 & 6 \end{array}\right]=B $$ (a) Use matrix multiplication to find a matrix giving the comparative cost per bakery item for the two purchase options. (b) Suppose a day's orders consist of 20 dozen sweet rolls, 200 loaves of bread, 50 cakes, and 60 pies. Write the orders as a $1 \times 4$ matrix, and, using matrix multiplication, write as a matrix the amount of each ingredient needed to fill the day's orders. (c) Use matrix multiplication to find a matrix giving the costs under the two purchase options to fill the day's orders.
Systems and Matrices
Properties of Matrices
The Bread Box, a small neighborhood bakery, sells four main items: sweet rolls, bread, cakes, and pies. The amount of each ingredient (in cups, except for eggs) required for these items is given by matrix $A$. The cost (in cents) for each ingredient when purchased in either large lots or small lots is given in matrix $B$. (a) Use matrix multiplication to find a matrix giving the cost per item for the two purchase options. (b) Suppose a day's orders consist of 20 dozen sweet rolls, 200 loaves of bread, 50 cakes, and 60 pies. Write the orders as a 1 $\times 4$ matrix, and using matrix multiplication, write as a matrix the amount of each ingredient needed to fill the day's orders. (c) Use matrix multiplication to find a matrix giving the costs under the two purchase options to fill the day's orders. FIGURE CANNOT COPY.
Matrix Properties and Operations
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