Question

M5_8. Cullowhee Manufacturing manufactures kitchen sinks that are made out of a composite material. The production of these sinks utilizes three processes – molding, finishing, and painting. The number of units that can be processed by each of these processes in an hour is shown below:

Process	Output(units/hour
Molding	7
Finishing	12
Painting	10

This is a sequential process – so products cannot be finished if they have not been molded; products cannot be painted if they have not been finished (Hint: constraints- the number of finished products must be the same as the number of molded products?). The labor costs per hour are $11 for molding; $13 for finishing; and $15 for painting. Cullowhee manufacturing has a maximum labor budget of $4000 per week. A total of 120 hours of labor is available for each of the three processes per week. Each completed sink requires 9 pounds of the composite material and the company has a total of 8,000 pounds of this material available every week (Hint: how much material is used in one hour in Molding?). Each sink earns a profit of $125 (Hint: the profit for this situation is based on the number of products that are painted). The manager of Cullowhee Manufacturing wants to know how many hours per week to run each process to maximize profit. (Note: Product mix problems usually have decision variables that represent the number of products to make – this is a situation where the decision variables represent the number of hours to run each department)

1. a) What is the expected profit (the value of the objective function)?

2. b) Based on your solution, how many hours should molding operate per week (enter as an

   integer)?

3. c) Based on your solution, how many hours should finishing operate per week (enter as an

   integer)?

4. d) Based on your solution, how many hours should painting operate per week (enter as an

   integer)?

5. e) If you could additional hours to one department (e.g. increase from 120 per week to something

   greater than 120 per week) to improve the objective function – which department would you

   add additional hours of capacity?

6. f) How many sinks are they producing per week (you need to calculate this using information from

   your optimal solution.

   Submit the Word document with the formulation for Problem M5.8 (decision variables, objective function, constraints in standard format as specified/demonstrated in videos). Submit Excel file with solution for M5.8 using LP Template

Answer 1

	per hour	cost per hour		Cost for 120 hours	total items made
molding	7	11		1320		840(because this is the maximum can be produced of 120 hours of molding)
finishing	12	13		1560
painting	10	15		1800
	max budget for week for labour	4000$
	total hours of work per each proc	120 hours
	total material available per week	8000 pounds
	material used for 1 sink		9 pounds
	Each sink profit is		125$
1) how much material used for 1 hour molding	63
2) Total 120 hours of work required material	7560
3)cost of 120 hours of molding		1320
4)70 hours to finish 840 items moulded in120 hours
5) cost for 70 hours of finishing 910
6) 84 hours to paint 840 items finished
7)Cost for 84 hours of painting is 1260
8)Total budget to be given for 840 items is 3490 dollars a)total profit made made by 840 items are 1,05,000 $ (each 125 $) b)120 hours of molding required c)70 hours of finishing required d)84 hours to paint required e)Molding will be increased if given freedom to increase f)840 sinks will be produced.