Task 1 Your company is going to build a block of units on th

Task 1

Your company is going to build a block of units on the site costing up to $3 million. Local government has zoned the site for maximum of 10 units. Each2 bedrooms unit can be built for $250 000 and will return $800 a week in rent. Each3 bedrooms unit can be built for $350 000 and will return $1100 a week in rent. determine how many units of each type you should build for a maximum rental, assuming that all units are always rented.

Task 2

Your company is preparing a site for construction by excavating and removing earth. there is 420 cubic metres of earth to be removed off a block of block of land. You have two types of trucks available: trucks of 6 cubic metres that cost $60 per load to operate and trucks of 8 cubic metres that cost $70 per load. The smaller truck takes 6 mins to load and the larger truck takes 10 mins. The excavator must use both trucks but can load only one truck at a time and will stop operations after 8 hours. Work out what combination of trucks that will shift the earth in 8 hours for the smallest cost.

Solution

Post one more question to get the second answer

Task 1

Let the number of 2 bedroom units be x

Let the number of 3 bedroom units be y

Constraints:

250000x + 350000y <= 3000000

or it can be written as

5x + 7y <= 60

x+y<=10 (maximum number of units must be 10)

Profit Function:

z = 800x + 1100y

The maximum will occur when both x and y are equal to 5

Maximum weekend rent = 800x + 1100y

=> 800(5) + 1100(5)

=> 9500$