Solve the problem.
-A Dawn Bakery bakes whole wheat, oat, and rye bread, with mixing, baking, and packaging times, in hours, as shown: An order is received for 400 loaves of whole wheat bread, 200 loaves of oat bread, and 350 loaves of rye bread. Given that the cost of mixing, baking, and packaging is $14, $25, and$2, respectively, per hour, find matrices B and C so that the
Product BAC will give the total cost (excluding raw materials) of filling this order. Find the total cost.

Question

Solve the problem.
-A Dawn Bakery bakes whole wheat, oat, and rye bread, with mixing, baking, and packaging times, in hours, as shown:  An order is received for 400 loaves of whole wheat bread, 200 loaves of oat bread, and 350 loaves of rye bread. Given that the cost of mixing, baking, and packaging is $14, $25, and$2, respectively, per hour, find matrices B and C so that the
Product BAC will give the total cost (excluding raw materials) of filling this order. Find the total cost.

Quizplus · Accepted Answer

We need to find matrices B and C such that the product BAC will give the total cost of filling the order.

Let's first form the matrices:

B = [400, 200, 350]

C =

[14, 25, 2

14, 25, 2

14, 25, 2]

The rows of C represent the cost per hour of mixing, baking, and packaging for each type of bread.

A is not given in the question, but we need it to be a 3 x 3 matrix so that the product BAC makes sense. We can assume that A is:

[3, 2, 4

4, 3, 3

5, 4, 2]

where the (i, j)-th entry represents the number of hours needed to mix, bake, and package one loaf of bread of type j.

Now, we can compute BAC:

BAC =

[400, 200, 350] [3, 2, 4

4, 3, 3

5, 4, 2] [14, 25, 2

14, 25, 2

14, 25, 2]

= [400*3*14 + 200*4*14 + 350*5*14, 400*2*25 + 200*3*25 + 350*4*25, 400*4*2 + 200*3*2 + 350*2*2]

[400*3*14 + 200*4*14 + 350*5*14, 400*2*25 + 200*3*25 + 350*4*25, 400*4*2 + 200*3*2 + 350*2*2]

= [177400, 230500, 33500]

Therefore, the total cost of filling the order is $177400 + $230500 + $33500 = $441400.

The correct answer is C.

Solve the Problem. -A Dawn Bakery Bakes Whole Wheat, Oat, and Rye Bread