Challenge 2. For construction of a bridge deck, a contractor has found natural r
ID: 2074106 • Letter: C
Question
Challenge 2. For construction of a bridge deck, a contractor has found natural reserves of sand and gravel at Bloomingdale and Valley Springs where he may purchase such material. The unit cost including delivery from Bloomingdale and Valley Springs is $5 and $7, respectively. In addition to material cost there is a loading cost of about $1.5 for every 1 m of material loaded at each pit. After the material is brought to the site it is mixed thoroughly and uniformly, and contract specification state that the mix should contain a minimum of 45,000 m) gravel. The Bloomingdale Pt contains 35% sand and the Valley Springs Pt contains 40% sand. Assume b and u are variables used to indicate the total material in m) taken to the construction site from Bloomingdale and Valley Springs respectively For the following questions recall that an engineering based function is an equation that can take any form for example: y = f(ax), f(a, x). ra, x).etc., where, for example, y, x can be variables, ..B constants, and fc) any functional form Question 2.a. Develop an engineering-based cost model for the total cost associated with bringing material from the two pits to the construction site Question 2.c. Develop two engineering-based functions to indicate the mix should contain a minimum of 5,000 m gravel Question 2.d. Which of the following options is the most desirable? a. Bring 150,000 m from Bloomingdale, 0 from Valley Springs b. Bring 35,000 m2 from Bloomingdale, 35,000 from Valley Springs c. Bring 0 m from Bloomingdale, 75,000 from Valley SpringsExplanation / Answer
let b= Material taken to construction site from Bloomingdale in m3
v= Material taken to construction site from Valley Spring in m3
2.a.) Engineering based cost model for the total cost associated with bringing the material form the two pits to the construction site is
Min z = 5b+7v+1.5(b+v)
( since cost for material from Bloomingdale is 5$ and cost for material from Valley spring is $7 and $1.5 for both the sites for loading)
2.c) Engineering based function to indicate the mix should contain a minimum of 45,000m3 gravel is
0.65b+0.6v < 45,000 (constraint) and b,v > 0
Other equation cannot be obtained since there is only a content of minimun quantity of gravel is given the question needs additional data
2.d From the above cost equation Min z = 5b+7v+1.5(b+v) we check by placing the values of b and v in it and the minumum value obtained will be the desired one
a. z=5*150000+7*0+1.5(150000+0) = $975,000
b. z=5*35000+7*35000+1.5(35000+35000) = $525,000
c. z=5*0+7*75000+1.5(0+75000) = $637,500
Since from the above observation we find that bringing 35000m3 form Bloomingdale and 35000m3 from Valley Spring is most desirable