Using proportions, the costs are given as follows:
a) Total Labor Cost: $2,505,600.
b) Total Product Cost: $1,950,000.
c) Total Cost = $4,455,600.
d) Cost per home = $461.77.
e) Cost per week = $99,013.33.
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For item a, the labor cost is found using the <u>earnings of the workers</u>, as follows:
45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)
Hence:
Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.
For item b, the product cost is the <u>cost of the boards</u>, hence:
(175 + 150 + 50 boards) x 5,200
Total Product Cost = 375 x 5,200 = $1,950,000.
For item c, the total cost is the <u>sum of the product cost and the labor cost,</u> hence:
Total Cost = 2,505,600 + 1,950,000 = $4,455,600.
For item d, the cost per home is found dividing the <u>total cost by the 9,649 homes</u>, hence:
Cost per home = 4455600/9649 = $461.77.
For item e, the cost per week is found dividing the <u>total cost by the 45 weeks</u>, hence:
Cost per week = 4455600/45 = $99,013.33.
More can be learned about proportions at brainly.com/question/24372153
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