a$.$ A contractor pays his subcontractors a fixed fee plus mileage for work performed. On a given day the contractor is faced with four electrical jobs associated with various projects. He has four electrical subcontractors which are located at various places throughout the area. Given below are the distances between the subcontractors and the projects: $$ Project Subcontractor$$ A B C D Westside $10151618$ Federated $14131610$ Goliath $119818$ Universal $1313119$ Required: $$ How should the contractors be assigned to minimize total costs?$$ b$.$ A company has orders for $80$ tons of bricks at three locations A$,$ B and C as follows: A $25$ tons, B $45$ tons, and C $10$ tons. The company has two plants, each of which can produce $50$ tons per week.$$ The delivery cost per ton is given in the following table: $$ A B C Plant $1243040$ Plant $2304042$ Required: i$.$ Find initial basic feasible solution using either the Least Cost method or Vogel$$s Approximation Method $($VAM$).$ ii$.$ Use the transportation simplex to determine the optimal delivery schedule. $$