A: Cost of Labor: Let x% be done by person and y% be done by equipment We are gi

Question

A:

Cost of Labor:

Let x% be done by person and y% be done by equipment

We are given 10% must be done by equipment and 20% must be done by labor

Therefore x>20 ……………………………………………………………………………………………………………….a

y>10…………………………………………………………………………………………………………………………………b

also x+y = 100 ………………………………………………………………………………………………………………….c

Next we are also given

100,000 person hrs = 4% of project work which means project work in total = 2500,000 person hrs

And Labor = 5 M / 100,000 person hrs which means project cost if done by labor = 25 M

So cost of labor = x% of 25 M = 25x

Similarly Cost of equipment:

10,000 equipment hrs = 2% of project work which means project work in total = 500,000 equipment hrs

But Max equipment hrs = 200,000 which is 200,000/500,000 = 40% of the total equipment hrs which translate to y <= 40………………………………………………………………………………………………………………………………..d

Now since the equipment cost is free we would get the max work done by equipment i.e 40% at ZERO cost

Rest 60% of the work would be done through labor which will cost us 25M * .6 = 15 M

So the total labor and equipment cost = 15 M

Cost of material:

We are given Material = 10 M /ton and in total we need minimum 52 tons

Let z be the tons of material so z>= 52 ………………………………………………………………………………………e

Also total cost i.e   15M + 10z <= 623 M

Which means z<= 60.8…………………………………………………………………………………………………………………f

Hence our total cost is 15 M + 10z which is our objective function subject to constraints e and f

B:

If 85% of the work must be done by labor then we have the rest 15% which is lesser than 40% and greater than 10 % (our constraints d and b) done for FREE

Cost of labor = 25 M * .85 = 21.25 M

Cost of Material = 10z

Total cost = 10z +21.25 M

Explanation / Answer

Can someone please solve parts a and b for me please, and clearly identify the objective function along with its constraints if its a linear programming problem! 'LMN' refers to 623 and 'KM' refers to 52.

2) Due to a combination of political, economic, legal and ethical considerations, the governor has decided to build the canal. This is a huge operation that will cost a lot, but exactly how much depends on some specific decisions that have to be made. Voters have promised up to SLMN million in bonds. The main costs associated with the project are for labor, equipment and materials. You can buy as much labor and materials as desired, but the equipment fleet is fixed. Cost of materials is $10 million per ton, cost of labor is $5 million per 100,000 person hours and there are 200,000 equipment hours available. To complete the project requires a minimum of KM tons of materials. Each 100,000 person hours contributes 4% towards project completion and each 10,000 equipment hours contributes 2% towards completion, and 10% of the work must be done by equipment while 20% of the work must be done by labor. The remaining work can be done by people or equipment. Since the state already owns the equipment, ts use is essentially free. a) What is the cost for completing the project? b) If new labor union agreements specify that 85% of the 30/ 20work must be done by people, how will this affect the project? (be numerically specific

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