Optimization problem \"NUMBER 4\" Set up and solve the problem on a spreadsheet.

Question

Optimization problem "NUMBER 4"

Set up and solve the problem on a spreadsheet. What is the optimal solution? Explain the rationale for the solution. Fiber Tech makes newsprint for newspapers at three mills. A, B, and C. The cost of producing newsprint is estimated to be $210 at mill A, $225 at B, and $220 at C. Five primary geographical markets are served from these mills. The monthly demand at each market, the shipping cost (per ton) between each mill and market, and the monthly production capacity of each mill are given in the table. Fiber Tech would like to assign production responsibilities to the mills, and also specify how much should be shipped from each plant to each market, so as to minimize total production and distribution costs. Formulate an LP to minimize total production and distribution costs. Set up and solve the problem on a spreadsheet. What is the optimal solution? Explain the rationale for the solution. Northwest Pipe (NP) makes water pipe. NP is planning , the next seven months, March through September.

Explanation / Answer

The given question is a transportation problem and includes the cost of manufacturing has to included into it

By including the cost of manufacturing and transportation the matrix will be

A 230 235 240 225 245 Capacity 1200 ( New row is 210+ transportation cost)

B 255 245 257 253 244 Capacity 1500 (New row is 225+ transporation COst)

C 245 238 248 243 251 Capacity 900

Demand 600,100,500,800,500

LPP is

Minimize Z= 230X11+235X12+240X13+225X14+245X15+255X21+245X22+257X23+253X24+244X25+245X31+238X32+248X33+24X34+251X35

Subject to

230X11+235x12+240x13+225x14+245x15=1200

255x21+245x22+257x23+253x24+244x25=1500

245x31+238x32+248x33+243x34+251x35=900

( First three condition are towardws row side, next five equations are towards bottom side)

230x11+255x21+245x31=600

235x12+245x22+238x32=100

240x13+257x23+248x33=500

225x14+253x24+243x34=800

245x15+244x25+251x35 =500

Xij>= 0 where i=1,2,3 and J= 1,2,3,4,5

( Hint to student please write the given table by adding 210 to A , 225 TO B and 220 to C, Since objective function is minimize total transpost+production cost minimise the entire matrix value, suject to the constrain of demand and supply.)

Solver Solution is

1 2 3 4 5 Capacity Total A 400 0 0 800 0 1200 1200 B 0 0 0 0 500 1500 500 C 200 100 500 0 0 900 800 Demand 600 100 500 800 500 total 600 100 500 800 500

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.