Need help with mathematical statement based on the problem below (I know how to

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Need help with mathematical statement based on the problem below (I know how to do the network representation):

Here is an example of a mathematical statement for another problem we practiced on:

Here is an example of a network representation for another problem we practiced on:

Here is data table for the problem I need help on (mathematical statement):

2nd part of data for the problem I need help on (mathematical statement):

Case Problem 2 SUPPLY CHAIN DESIGN The Darby Company manufactures and distributes meters used to measure electric power consumption. The company started with a small production plant in El Paso and gradu- ally built a customer base throughout Texas. A distribution center was established in Fort Worth, Texas, and later, as business expanded, a second distribution center was established in Santa Fe, New Mexico The El Paso plant was expanded when the company began marketing its meters in Arizona, California, Nevada, and Utah. With the growth of the West Coast business, the Darby Company opened a third distribution center in Las Vegas and just two years ago opened a second production plant in San Bernardino, California. Manufacturing costs differ between the company's production plants. The cost of each meter produced at the El Paso plant is $10.50. The San Bernardino plant utilizes newer and more efficient equipment; as a result, manufacturing costs are $0.50 per meter less than at the El Paso plant. Due to the company's rapid growth, not much attention had been paid to the efficiency of its supply chain, but Darby's management decided that it is time to address this issue. The cost of shipping a meter from each of the two plants to each of the three distribution centers is shown in Table 6.10 The quarterly production capacity is 30,000 meters at the older El Paso plant and 20,000 meters at the San Bernardino plant. Note that no shipments are allowed from the San Bernardino plant to the Fort Worth distribution center The company serves nine customer zones from the three distribution centers. The fore- cast of the number of meters needed in each customer zone for the next quarter is shown in Table 6.11

Explanation / Answer

So

Obj func:

Min Z = (10.5)*(x11+x12+x13)+(10)*(x22+x23)+ 3.2*x11+2.2*x12+4.2*x13+3.9*x22+1.2*x23 + 0.3*x31+5.2*x41+ 2.1*x32+5.4*x42+ 3.1*x33+4.5*x43 + 4.4* x34+ 6*x44+ 6*x35+ 2.7*x45+5.4*x55+ 4.7*x46 + 3.3*x56+ 3.4*x47+2.4*x57 + 3.3*x48 + 2.1* x58 +2.7*x49+ 2.5*x59

S.t

(x11+x12+x13) <= 30000

(x22+x23) <= 20000

x11 =

x12 + x22 =

x13+ x23 =

x31+x41 >= 6300

x32+x42 >= 4880

x33+x43 >= 2130

x34+x44 >= 1210

x35+x45 >= 6120

x55+x46 +x56 >= 4830

x47+x57 >= 2750

x48 + x58 >= 8580

x49+ x59 >= 4460

All dec var >=0

Production rate Max capacity El Paso 10.5 30000 San B 10 20000 Cost FW SF LV El Paso 3.2 2.2 4.2 San B 3.9 1.2 Cost D SA W KC D SLC P LA SD FW 0.3 2.1 3.1 4.4 6 SF 5.2 5.4 4.5 6 2.7 4.7 3.4 3.3 2.7 LV 5.4 3.3 2.4 2.1 2.5 Demand 6300 4880 2130 1210 6120 4830 2750 8580 4460

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