Question 1 A Highway contractor has four locations A, B, C, and D on a road contract which crushed stone is to be delivered. The stone, which is all of the same quality is to be supplied from three quarries 1, 2, and 3. The table below shows the relative transportation cost per cubic meter of transporting stone from each quarry to each site. Location Quarry output (m³) Quarry A D Relative transportation costs ($ per m') 1 10 15 11 120 12 8. 6. 3 255 3 10 6. 13 60 45 105 150 135 Quantities required at each location (m³) a) What is the optimal allocation of the crushed stone from each quarry to each location?

A Highway contractor has four locations A, B, C, and D on a road contract which crushed stone is to be delivered. The stone, which is all of the same quality is to be supplied from three quarries 1, 2, and 3. The table below shows the relative transportation cost per cubic meter of transporting
stone from each quarry to each site.

However, the contractor discovered a technical problem in the third quarry, which results in a temporary shutdown of the facility. Based on this new condition, the contractor must deliver the crushed stone from the first and the second quarries only. Any shortage in the required crushed stone has to be covered from an external source.  

a) What is the optimal allocation of the crushed stone from each quarry to each location under the new circumstances?
b) What is the transportation cost corresponding to the solution obtained in part a?
c) Which of the four sites are affected by the shortage that results from the shutdown of the third quarry?