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Course Number & Title: MGT4310  Operations Management HOMEWORK 4 1

Operations Management

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Course Number & Title: MGT4310  Operations Management

HOMEWORK 4

1. Andy Mendoza makes handcrafted dolls, which he sells at craft fairs. He is considering massproducing the dolls to sell in stores. He estimates that the initial investment for plant and equipment will be $20,000, while labor, materials, packaging, and shipping will be about $8 per doll. He has determined that monthly sales volume is related to price, according to the following equation:

 

? = 5000 − 90?

 

1. Develop the nonlinear profit function as a function of price.
2. Find the optimal price, the optimal volume per month, and the maximal profit per month.

 

 

2. Metro Telcom Systems develops, sells, and install computer systems. The company has divided its customer base into five regions, and it has 15 representatives who sell and install the company’s systems. With its daily expense budget of $65,000, the company wants to allocate salespeople to regions so that they maximize daily sales revenue. However, whereas the sales increase as the number of salespeople allocated to a region increases, they do so at a declining rate, according to the nonlinear formula as follows.

 

?

????? ????? = ? −    

?

 

  where ? is the number of salespersons allocated to region ?. Following are the parameters ? and ? for daily sales in each region and the daily expense (including all costs) per representative for each region:

 

			Region
	A	B	C	D	E
? ($) Parameter ? ($)	16,000 8,000	24,000 14,000	9,000 5,000	12,000 6,000	21,000 13,000
Daily expense  for each region ($)	440	550	240	315	450

 

   (a) Formulate a nonlinear programming model for this problem with integer decision variables.

 

             

3. Home-Base, a home improvement and building supply chain, is going to build a new warehouse facility to serve its stores in six North Carolina cities – Charlotte, Winston-Salem, Greensboro, Durham, Raleigh, and Wilmington. The coordinates of these cities (in miles), using Columbia, South Carolina, as the graphical origin (0,0), and the annual truckload trips that supply each store are as follows:

 

 

Coordinate

 

Store	x	y	Truckload trips
1. Charlotte	15	85	150
2. Winston-Salem	42	145	90
3. Greensboro	88	145	180
4. Durham	125	140	150
5. Raleigh	135	125	200
6. Wilmington	180	18	160

 

   (a) Formulate a nonlinear programming model for this problem using Euclidean distance and real-valued decision variables.