Reference no: EM13844034

Problem about operation research

Problem by AMPL program

I need to

variable

objective

constriction

for this problem

Make sure should be write variable and objective and constriction for each part

there is two part (a) and (b)

A machine shop makes small-run, precision woodworking tools on the following machines:

• Four Grinders
• Two Drill Presses
• Three Lathes
• One Borer
• One Planer

Each product generates a certain amount of gross profit (defined as the selling price less the cost of raw materials and manufacturing). These quantities, together with the time required from each machine for manufacture (in hours) are given in the table below. A dash indicates that the product does not need that particular machine as part of its manufacturing process.

Tool Produced	Gross profit	Grinder	Drill Press	Lathe	Borer	Planer
Dowelling Jig	10	0.5	0.1	0.2	0.05
Square	6	0.7	0.2		0.03
Kerf Ruler	8	-	-	0.8	-	0.01
Tenon Jig	4		0.3	-	0.07	-
Saw Aligner	11	0.3			0.1	0.05
Center Scribe	9	0.2	0.6
Honing Guide	3	0.5		0.6	0.08	0.05

There are limitations on how many of each tool the manager believes the company can sell in each month. Unfortunately, during the next 6 months (Jan - June), certain machines will have to be taken offline for maintenance. The limit to demand and maintenance schedule can be found in the table below

	Dowelling Jig	Square	Kerf Ruler	Tenson Jig	Saw Aligner	Center scribe	Horning guide	Tools Offline
January	500	1000	300	300	800	200	100	1 Grinder
February	600	500	200	0	400	300	150	2 Lathes
March	300	600	0	0	500	400	100	1 Borer
April	200	300	400	500	200	0	100	1 Drill Press
May	0	100	500	100	1000	300	0	1 Grinder and 1 Drill Press
June	500	500	100	300	1100	500	60	1 Planer and 1 Lathe

It is possible to store up to 110 of any completed tool at any time at a cost of 40c per unit per month. There are no tools in stock at the moment, but management would like to have 50 of each tool on hand at the end of the 6 months. The factory works two 8-hour shifts a day, 6 days a week, 25 days a month.

(a) Formulate a linear program to determine the production schedule that maximizes profit?

(b) Someone has suggested that, instead of having the machine maintenance schedule as it is, could the schedule be rearranged to improve profit? Copy and modify your original model to accom¬modate these changes.