Question
In: Statistics and Probability
Laura is planning to buy five 5-lb bags of sugar, four 5-lb bags of flour, five...
Laura is planning to buy five 5-lb bags of sugar, four 5-lb bags of flour, five 1-gal cartons of milk, and four 1-dozen cartons of large eggs. The prices of these items in three neighborhood supermarkets are as follows.
| Sugar (5-lb bag) |
Flour (5-lb bag) |
Milk (1-gal carton) |
Eggs (1-dozen carton) |
|
|---|---|---|---|---|
| Supermarket I | $3.15 | $3.79 | $2.99 | $3.49 |
| Supermarket II | $2.99 | $2.89 | $2.79 | $3.29 |
| Supermarket III | $3.74 | $2.98 | $2.89 | $2.99 |
(a) Write a 3 × 4 matrix A to represent the prices (in dollars) of the items in the three supermarkets.
| A = |
|
|||||||||||||||||||||||||||||||||||||||||||||||||
(b) Write a 4 × 1 matrix B to represent the quantities of
sugar, flour, milk, and eggs that Laura plans to purchase in the
three supermarkets.
| B = |
|
||||||||||||||||
(c) Use matrix multiplication to find a matrix C that
represents Laura's total outlay (in dollars) at each
supermarket.
| C = |
|
|||||||||||||
(d) At which supermarket should she make her purchase if she wants
to minimize her cost? (Assume that she will shop at only one
supermarket.)
supermarket I or supermarket II or supermarket III?
Solutions
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