Question 379957: A new mall with 2 major department stores and 55 speciality shops is being built. You are a subcontractor in charge of planning and builiding the parking lots for the mall. The planners provide you with the following information:
-The total number of parking spaces must range from 2,000 to 2,400 spaces.
-For every employess parking space there must at least 9 public parking spaces.
-There must be atleast 20 employee parking parking spaces per department store and 2 employee parking spaces per specialuty shop.
You anticipate that the building costs will be $580 per public parking space and $600 per employee parking place.
The mall planners expect that, during an average week, revenue from each public space will be at least $1,000 and from each employee parking space will be $100.
How many parking spaces of each type should be built to minimize the cost of the building of the parking lot? How many parking spaces of each type should be built to maximize weekly revenue?
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! From the given information there must be at least:
40 employee parking spaces for the department stores
110 employee parking spaces for the specialty stores
150 employee parking spaces in total
1350 public parking spaces
To minimize building costs, let all of the remaining parking spaces be public. Since there are at least 150 employee parking spaces we can assume that 1,850 public spaces will exist there. The cost will be (150)(600) + (1850)(580) = $1,163,000.
To maximize weekly revenue, we should still let all the remaining parking spaces be public, and use all 2,400. In this case the weekly revenue is (150)(100) + (2250)(1000) = $2,265,000.
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