Advising a building contractor

Question

A building contractor has acquired a 10 acre site and plans to develop it as a residential area. The contractor has two basic designs for homes: a low income home and a middle income home. he expects to take 5 years to complete the project. 

 

Low income homes cost 30,000 to build at a density of a 20 homes per acre, whereas middle income homes cost 40,000 to build at a density of 12 homes per acre. The contractor expects to sell a maximum of 100 low income homes and 75 middle income homes, but the zoning regulations will allow no more than a total of 155 homes on site. The local city council has also stipulated a formula to ensure that sufficient low income homes are constructed. This formula stipulates: the number of low income units shall be at least 35 units greater than half the number of middle income units. The contractor employs a work force of 60 people. The architect estimates that it will take a 2.0 labor years to build a low income home and a 2.5 labor years to build a medium income home.

 

The contractor expects to sell a low income home for 50,000 and a medium income home for 70,000. Your task is to advise the contractor. How many of each type of home should he build? 

Answer 1

Solving this problem fall to the value and formula from the city council.

The total number of houses is 155.

The number of low income homes should be  equal to half of the middle income homes +35.

So: let x = the number of middle class homes

then : 155 - x = the number of lower class homes this also x/2 + 35

 

solve for x:

155 - x = x/2 + 35 

2(155-x) = 2(x/2) + 2(35)              multiply by 2

310 - 2x = x + 70                          simplify

(310 - 2x) - 70 = (x + 70) - 70        subtract 70

(240 - 2x) + 2x = (x) +2x               add  2x

240  = 3x

80  = x

So the number of middle income homes is 80.

and the number of low income homes is 155-80 or 75.

The rest of the information given is not used to solve this.