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r Programming B ome com https://blackboard.sdsu.edu/bbcswebdav/pid-277281 7-dt-content-rid-55263164-1/courses/BA360-05-Spring2016/MIS302-02-Summer2015-Imp AppsBookmarks EAIDUNK SDSU -Fin PSDSu Par SDSU Parking- Aztec-Organizational Beha- Bookshelf Support-u- P SERVICES TIMEUseful Links.on theWSDSU Career Se uareTrade . 4 16 4.A manufacturer of bathroom fixtures produces fiberglass bathtubs in an assembly operation consisting of three processes: molding, smoothing, and painting. The number of units that can be put through each process in an hour is as follows Process Molding Smoothing Painting Output (units/hr) 12 10 (Note: The three processes are continuous and sequential; thus, no more units can be smoothed or painted than have been molded.) The costs per hour are $18 for molding, $15 for smoothing and $ 16.50 for painting. The company's operating budget is $13000 per week. A total of 120 hours is available for all three processes per week. Each completed bathtub requires 90 pounds of fiberglass, and the company has a total of 10000 pounds of fiberglass available each week. Each bathtub earns a profit of $375. The manager of the company wants to know how many hours per week to run each process in order to maximize profit. Formulate and solve a linear programming model for this problem O Ask me anything 8:11 PM 4/8/2016

Explanation / Answer

4. Decision variables: let x be the number of hours spent on Molding

Objective function: MAximize profit

Line production/hour = 7 units

Weekly production = 7 units/hr * x hours

Thus, Profit = 375 * 7x

Objective Function: Maximize (375*7*x)

Constraints:

molding 1 bathtub takes 0.14 hours (1/7), smoothing takes 0.08 hours(1/12) and painting takes 0.10 hors(1/10)

(NOTE: Processing time / unit = 1 hour/ hourly production)

Fining the ratio we get, molding 7 bathtubs takes one hour, smoothing 7 bathtubs will take 0.08 hrs*7 = 0.6 hors, similarly, painting 7 bathtubs will take 0.10*7 = 0.7 hours

Hence time processing time for the 3 processes will be in ratio: 1: 0.6 : 0.7

hence, time required for smoothing = 0.6*x

and, time required for painting = 0.7 *x

1. x>=0 (non negativity constraint)

2. x+0.6 x+0.7 x <=120 (total working hours constraint)

3. 18 x+ 15 (0.6 x) + 16.5 (0.7 x) <= 13000 (total cost should be less than of equal to the available budget constraint)

4. 90 * (7x) <= 10000 (fiber glass constraint: fiberglass/bathtub * weekly production <= total available fiberglass)

Solving th eLP in Excel Solver:

Processes output (units/hr) time (hrs) req/bathtub costs($/hr) hrs/week Ratio total cost (cost/hr*hrs/week) Molding 7 0.14 18 15.87 1.0 285.7 Smoothing 12 0.08 15 9.26 0.6 138.9 Painting 10 0.10 16.5 11.11 0.7 183.3 0.33 36.24 607.9 no of bathtubs produced in a week will be no of bathtubs molded, hence hrs/week for molding * 7 units/hr Weekly production 111 Budget 13000 $ total avail time 120 hours fiberglass/bathtub 90 pounds tot ifbre glass needed 10000 (=fiberglass/ bathtub*weekly production) total avail. fiberglass 10000 pounds profit/bathtub 375 $ profit $ 41666.67

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