Applications Involving Matrices Our last day in Sec

Applications Involving Matrices… Our last day in Sec. 7. 2…

Right in with practice problems…: Happy Valley Farms produces three types of eggs: 1 (large), 2 (X-large), 3 (jumbo). The number of dozens of type i eggs sold to grocery store j is represented by aij in the matrix The per dozen price Happy Valley Farms charges for egg type i is represented by bi 1 in the matrix Find the product B T A

Right in with practice problems…the “Do Now”: What does this product represent? ? ? Each element in the product represents the total income Happy Valley Farms makes at grocery store j, selling all three types of eggs.

A company sells four models of one name brand “all-in-one fax, printer, copier, and scanner machine” at three retail stores. The inventory at store i of model j is represented by s ij in the matrix The wholesale and retail prices of model i are represented by pi 1 and pi 2 , respectively, in the matrix Determine the product SP. What does this matrix represent?

The wholesale and retail values of all the inventory at store i are represented by a i 1 and a i 2 , respectively, in the matrix SP.

A building contractor has agreed to build six ranch-style houses, seven Cape Cod-style houses, and 14 colonial-style houses. The number of units of raw materials that go into each type of house are shown in the matrix Steel Wood Glass Paint Labor Ranch R = Cape Cod Colonial 5 7 6 22 20 27 14 10 8 7 9 5 17 21 13 Assume that steel costs $1600 a unit, wood $900 a unit, glass $500 a unit, paint $100 a unit, and labor $1000 a unit. 1. Write a 1 x 3 matrix B that represents the number of each type of house to be built.

A building contractor has agreed to build six ranch-style houses, seven Cape Cod-style houses, and 14 colonial-style houses. The number of units of raw materials that go into each type of house are shown in the matrix Steel Wood Glass Paint Labor Ranch R = Cape Cod Colonial 5 7 6 22 20 27 14 10 8 7 9 5 17 21 13 Assume that steel costs $1600 a unit, wood $900 a unit, glass $500 a unit, paint $100 a unit, and labor $1000 a unit. 2. Write a matrix product that gives the number of units of each raw material needed to build the houses.

A building contractor has agreed to build six ranch-style houses, seven Cape Cod-style houses, and 14 colonial-style houses. The number of units of raw materials that go into each type of house are shown in the matrix Steel Wood Glass Paint Labor Ranch R = Cape Cod Colonial 5 7 6 22 20 27 14 10 8 7 9 5 17 21 13 Assume that steel costs $1600 a unit, wood $900 a unit, glass $500 a unit, paint $100 a unit, and labor $1000 a unit. 3. Write a 5 x 1 matrix C the represents the per unit cost of each type of raw material.

A building contractor has agreed to build six ranch-style houses, seven Cape Cod-style houses, and 14 colonial-style houses. The number of units of raw materials that go into each type of house are shown in the matrix Steel Wood Glass Paint Labor Ranch R = Cape Cod Colonial 5 7 6 22 20 27 14 10 8 7 9 5 17 21 13 Assume that steel costs $1600 a unit, wood $900 a unit, glass $500 a unit, paint $100 a unit, and labor $1000 a unit. 4. Write a matrix product that gives the cost of each house.

A building contractor has agreed to build six ranch-style houses, seven Cape Cod-style houses, and 14 colonial-style houses. The number of units of raw materials that go into each type of house are shown in the matrix Steel Wood Glass Paint Labor Ranch R = Cape Cod Colonial 5 7 6 22 20 27 14 10 8 7 9 5 17 21 13 Assume that steel costs $1600 a unit, wood $900 a unit, glass $500 a unit, paint $100 a unit, and labor $1000 a unit. 5. Compute the product BRC. What does this matrix represent? This is the building contractor’s total cost of building all 27 houses.

And now for a review of the properties of matrices: Let A, B, and C be matrices whose orders are such that the following sums, differences, and products are defined. 1. Commutative Property Addition: A+B=B+A Multiplication: (Does not hold in general) 2. Associative Property Addition: (A + B) + C = A + (B + C) Multiplication: (AB)C = A(BC)

And now for a review of the properties of matrices: Let A, B, and C be matrices whose orders are such that the following sums, differences, and products are defined. 3. Identity Property Addition: A+O=A Multiplication: order of A = n x n A I n = In A = A 4. Inverse Property Addition: A + (–A) = O Multiplication: order of A = n x n – 1 AA = A A = I , |A| = 0 n

And now for a review of the properties of matrices: Let A, B, and C be matrices whose orders are such that the following sums, differences, and products are defined. 5. Distributive Property Multiplication over Addition A(B + C) = AB + AC (A + B)C = AC + BC Multiplication over Subtraction A(B – C) = AB – AC (A – B)C = AC – BC