A firm makes product X and Y Product X takes 2 hours each on

A firm makes product X and Y. Product X takes 2 hours each on machines L and M; product Y takes 3 hours on machine L and 2 hours on machine M. Machine L can be used for at most 10 hours and machine M for at most 8 hours. Profit for product X is $7 per unit, and $10 per unit for product Y. Let x be the number of units of product X produced, and let y be the number of units of product Y produced. State the liner programming problem that would help you find the maximum profit (state objective function and constraints) What is the second row of the product AB, if A = [0 3 5 -2 1 2], B = [2 1 0 4 - 1 3 2 2]

Solution

Q1)

Let the number of X units produced be x

Let the number of Y units produced be y

Profit Function Z = 7x + 10y

Constraints:

2x + 3y <= 10

2x + 2y <= 8

x>=0,y>=0

solving the equation we get x=2 and y=2 as the optimal solution

Profit Z = 7x + 10y = 7*2 + 10*2 = 34$

2)

Matrix A is of dimension 3X2 and Matrix B is of dimension 2X4

Hence the final matrix product AB will be of dimension 3X4

For calculating the second row, it will have four elements

First element: 5 * 2 + (-2)*(-1) = 12

Second element: 5 * 1 + (-2)*3 = -1

Third element: 5 * 0 + 2 * (-2) = -4

Fourth element: 5 * 4 + 2 * (-2) = 16

Hence the row is [12 -1 -4 16]