An engineering company is planning a project that requires careful allocation of work hours across three critical tasks: design (x), fabrication (y), and testing (z). The project manager provides the following data:
– The total work hours allocated for design, fabrication, and testing is 9 hours.
– Twice the design hours minus the fabrication hours plus the testing hours equals 5.
– Three times the design hours plus the fabrication hours minus twice the testing hours equals 1.
(a) Construct the system of linear equations based on the provided data.
(b) Solve the system of equations systematically.
(c) Discuss the feasibility of the solution, considering that all allocated work hours must be non-negative.
Question
From the provided project data, formulate the system of equations representing the allocation of work hours for the three tasks:
– Equation 1: The sum of design, fabrication, and testing hours equals 9.
– Equation 2: Twice the design hours minus fabrication hours plus testing hours equals 5.
– Equation 3: Three times the design hours plus fabrication hours minus twice the testing hours equals 1.
Hint
Hint
Hint
Carefully translate each bullet point into an algebraic equation.
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Answer
Answer
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Explanation
Explanation
- Formula Booklet
Complete Answer
The system of equations is: \(x + y + z = 9\), \(2x – y + z = 5\), and \(3x + y – 2z = 1\).
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Answer Explanation
Answer Explanation
Question
Solve the system of equations below:
\(x + y + z = 9\)
\(2x – y + z = 5\)
\(3x + y – 2z = 1\)
Hint
Hint
Hint
Use substitution or elimination to eliminate one variable and solve step by step.
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Answer
Answer
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Explanation
Explanation
- Formula Booklet
Complete Answer
\(x = 2, \; y = 3, \; z = 4\)
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Answer Explanation
Answer Explanation
Question
Based on your solution \(x = 2, \; y = 3, \; z = 4\), discuss the feasibility of the resource allocation, considering that all work hours must be non-negative. Is this allocation realistic for a project schedule?
Hint
Hint
Hint
Check that each value is non-negative and consider if the hour allocation is practical.
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Answer
Answer
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Explanation
Explanation
- Formula Booklet
Complete Answer
Yes, the solution \(x = 2, \; y = 3, \; z = 4\) is feasible, as all values are non-negative and represent a realistic distribution of work hours among the tasks.
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Answer Explanation
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