Question

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?

Answer 1