Ms ENG1014 is working as a consultant for a company that installs street lamps. She is asked to install lamps along a street that is 500 metres long, with the lamps spread out lamps in 15 metre intervals along the street.Three companies have different deals:Company A: first lamp costs $100 to install, and each successive lamp costs $4 lessCompany B: first lamp costs $120 to install, and each successive lamp costs $5 lessCompany C: first 5 lamps cost $150 each, but every lamp after that only costs $13What is the total cost from each company? You should assume that the lamps can have negative costs

First, let's calculate how many lamps are needed. The street is 500 metres long and the lamps are placed every 15 metres. So, the number of lamps needed is 500/15 = 33.33. Since we can't have a fraction of a lamp, we'll round this up to 34 lamps.

Now, let's calculate the cost for each company:

Company A: The first lamp costs $100. Each successive lamp costs$4 less. So, the second lamp costs $96, the third$92, and so on. This forms an arithmetic sequence with a common difference of -$4. The sum of an arithmetic sequence can be found using the formula n/2 * (a + l) where n is the number of terms, a is the first term, and l is the last term. Here, n = 34, a = 100, and l = 100 - 4*(34-1) = -$32. Since the problem states that we can't have negative costs, we'll consider this as $0. So, the total cost for Company A is 34/2 * (100 + 0) =$1700.

Company B: The first lamp costs $120. Each successive lamp costs$5 less. So, the second lamp costs $115, the third$110, and so on. This forms an arithmetic sequence with a common difference of -$5. Here, n = 34, a = 120, and l = 120 - 5*(34-1) = -$45. Since we can't have negative costs, we'll consider this as $0. So, the total cost for Company B is 34/2 * (120 + 0) =$2040.

Company C: The first 5 lamps cost $150 each, so that's 5 *$150 = $750. Every lamp after that costs$13. So, the cost for the remaining 34 - 5 = 29 lamps is 29 * $13 =$377. So, the total cost for Company C is $750 +$377 = $1127.

So, the total cost for Company A is $1700, for Company B is$2040, and for Company C is $1127.