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Matrix and word problem

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A contractor employs carpenters, electricians, and plumbers, working three shifts per day. The number of labor-hours required for carpenters in shift 1 is 40 hours, electricians in shift 1 is 28 hours, and plumbers in shift 1 is 9 hrs. The number of labor-hours required for carpenters in shift 2 is 18 hours, electricians in shift 2 is 32 hours, and plumbers in shift 2 is 15 hours. The number of labor-hours required for carpenters in shift 3 is 10 hours, electricians in shift 3 is 15 hours, and plumbers in shift 3 is 5 hours. Labor in shift 1 costs $11.00 per hour, shift 2 $12.50 per hour, and shift 3 $13.90 per hour.

Write a matrix A that denotes the amount of labor-hours based on shifts and each type of labor (carpenter, electrician, or plumber).

Write a column vector B representing labor costs per shift.

Perform the multiplication AB and explain what this product represents.

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Solution Summary

This provides an example of setting up a matrix for a word problem.

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Matrix Word Problem

Please answer the following Matrix Word Problem, and number 10, 22, and 30. Please show all your work in steps.

When two kittens named Cauchy and Cliché were introduced into a household with Jamie (an older cat) and Musk (a dog), the interactions between animals were complicated. The two kittens liked each other and Jamie, but didn't like Musk. Musk liked everybody, but Jamie didn't like any of the other animals.

a. Write a matrix in which rows (and columns) 1, 2, 3, and 4 refer to Musk, Jamie, Cauchy, and Cliché. Make an element a 1 if the animal for that row likes the animal for that column, and otherwise make the element a 0. Assume every animal likes herself.

b.Within a few days, Cauchy and Cliché decided that they liked Musk after all. Write a matrix, as you did in part a, representing the new situation.

Please see the attached for the problems.

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