A company wants to locate a distribution center that will serve six of its major

Question

A company wants to locate a distribution center that will serve six of its major customers in a 30X30 mi area. The locations of the customers relative to the southwest corner of the area area given in the following table in terms of (x,y) coordinates (the x direction is east, the y direction is north). Also given is the volume in tons per week that must be delivered from the distribution center to each customer. THe weekly delivery cost c(i) for customer i depends on the volume Vi and the distance d(i) from the distribution center. For simplicity we will assume that this distance is a straight line distance. (this assumes that the road network is dense.) The weekly cost is given c(i)=0.5d(i)Vi, i=1,...,6. Find the location of the distribution center (to nearest mile) that minimizes the total weekly cost to service all 6 customers. Table: customer xlocation ylocation Volume(tons/week) 1 1 28 3 2 7 18 7 3 8 16 4 4 17 2 5 5 22 10 2 6 27 8 6

Explanation / Answer

You are not helping your cause by calling people who answer nerds, but I will help you despite this. First, set up your customer information in an array. cust = ... [1,28,3; 7,18,7; 8,16,4; 17,2,5; 22,10,2; 27,8,6]; Then, you should simply calculate the cost for every x,y co-ordinate. for xx = 1:30 for yy = 1:30 distance = sqrt( (xx - cust(:,2)).^2 + (yy - cust(:,3)).^2 ); cost(xx,yy) = distance' * cust(:,3); end end you can figure out the minimum cost and location from there (since it is your homework) Here is an added bonus, a contour plot of the cost per location with respect to the customers: [C,h] = contourf(cost); clabel(C,h,'Color','k','BackgroundColo

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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