1. 1100] A design calls for 670 mp of type 1 granular material for use as a subb

Question

1. 1100] A design calls for 670 mp of type 1 granular material for use as a subbase a roadway, and 75 mN of type 2 for use as a base undertay ent for soewalks along the roacway. Three (3) gravel pits are available to draw from. Two of these are very low due to a busy summer and the third has imited draw because t is already being tapped by an ongoing project. The availability and cost for each of the sources is as given in the table below GravelAvailability (type 1) Cost (type 2) sim2 28.00 Cost (type 1) Pit sim 12.00 15.00 320 Gravel pits A and B have a minimum purchase order of $1500 each but C has a minimum purchase order of $1000. Develop a linear program for determining the minimum cost approach for meeting the requirements. 2. 11501-Job Scheduling Problems or Project Management You are the project manager for a construction project and you must schedule the various jobs which must be completed before the project is finished. Some of the jobs can begin immediately but other jobs can only begin after others are completed For example, grading can begin immediately but laying a foundation must be delayed unti the grading is completed. known and the set of jobs which must be completed before each job can begin is known. Your objective is to find a schedule (i.e. beginning times and ending times) for all of the jobs such that no jobs begins before any of its predecessors are completed and the time when all jots are finished is minimized Formulate a linear programming model to solve the problem. The data below are for a project which ten jobs, the time it takes to complete each job is For the following problem, formulate the Math program as follows 2 Describe each constraint and the objective in one or two sentences 3. Provide the Math program in the standard form. Be sure to include the non-negativity constraints where necessary Job 6 days 5 days 15 days 10 days 5 days 7 days 12 days 7 days 6 days 1,3 23, 5 12.5 which activity i may start; for example S1 is the day job I may begin. Let be the day on Let XF be the earliest time (days) when all jobs have been completed Fall 2017 Homework 02. Page 1 of2 GNEG 5023-PO1 Operations Research

Explanation / Answer

1.

Quantity of type1 material required = 670 m3

Quantity of type2 material required = 75 m3

Type 1 Material:

As we observe the table given, the cost of material is increasing from pit A to C

So we have to choose materials in such a way that the total cost is minimum.

Therefore first we choose full quantity available from pit A = 300 m3

and then full quantity from pit B = 320 m3

balance required is = 670-300-320 = 50m3

let's consider the cost for pit c = 50*15 = 750$

but from pit c the minimum purchase order should be 1000 $

therefore min material that is to be taken from pit c = 46 m3

Remaining we take from pit b = 670-46-300 = 324 m3

Therefore, Material from pit a = 300m3 and cost = 3000 $

Material from pit b = 324 m3 and cost = 324*12 =3888 $

Material from pit c = 46 m3 and cost = 46 * 15 = 690$

Type 2 Material:

Material from pit c = 10m3 and cost = 32*10 = 320 $

Material from pit b = 35 m3 and cost = 35*28 = 980 $

Materia; from pit a = 30m3 and cost = 30*25 = 750 $

All together from pit c we are taking min purchase of 1010 $ that is satisfying.

and other two pits it is already satisfying min purchase order requirement.

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