A construction project involves huge quantity of earth work and has 5 quarries to get the earth from and the details of the costs and times from each quarry are given below.

T he owner of the first three quarries cannot give more than 3,000 m3 a day. Quantities of at least 2,000 m3 and 1,500 m3 have to be taken from Quarry 4 and 5 respectively.

T otal no. of dump trucks available with the project is 60 and targeted amount of earthwork per day is 8,000 m3. Average volume of a dump truck can be taken as 8m3. Formulate the linear programming model for this problem.

Description Unit Quarry 1 Quarry 2 Quarry 3 Quarry 4 Quarry 5 Time taken for a dump truck to reach the site minutes 30 45 35 25 20 Cost/m3 of earth work `. 80 100 85 75 70