Question 2 CWD Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 1 6 4 2 4 5 3 4 2 The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. (see image) If there are two possible answers one will suffice. Where necessary a range analysis must be shown.(convert to minutes) a) What is the optimal solution (in words)? b) An additional 4 hours of shaper time became available. Evaluate the effect? Explain c) Two hours of Grinder time was lost. Evaluate the effect? d) An additional 20 units of component 3 was requested. Evaluate the effect e) The demand for component 2 decreased by 30 units. Evaluate the effect f) Suppose that the profit contribution of component 1 increases to $9.00. What is the new optimal solution? g) Suppose that the profit contribution of component 3 decrease by $2.00 . Would the optimal solution change h) Is the problem degenerate? Explain! i) Are there alternative optima in this problem? Explain

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 1C

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Question 2
CWD Manufacturing makes three components for sale to refrigeration companies. The
components are processed on two machines: a shaper and a grinder. The times (in minutes)
required on each machine are as follows:

Machine

Component	Shaper	Grinder
1	6	4
2	4	5
3	4	2

The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than
200 units of component 3 can be sold, but up to 1000 units of each of the other components can
be sold. In fact, the company already has orders for 600 units of component 1 that must be
satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively.

(see image)

If there are two possible answers one will suffice. Where necessary a range analysis must be shown.(convert to minutes)
a) What is the optimal solution (in words)?

b) An additional 4 hours of shaper time became available. Evaluate the effect? Explain
c) Two hours of Grinder time was lost. Evaluate the effect?
d) An additional 20 units of component 3 was requested. Evaluate the effect
e) The demand for component 2 decreased by 30 units. Evaluate the effect
f) Suppose that the profit contribution of component 1 increases to $9.00.
What is the new optimal solution?
g) Suppose that the profit contribution of component 3 decrease by $2.00 . Would the optimal solution change
h) Is the problem degenerate? Explain!
i) Are there alternative optima in this problem? Explain

Transcribed Image Text:Microsoft Excel 14.0 Answer Report Report Created: 10/16/201525209 AM Result: Solver found a solution. All Constraints and optimality conditions are satisfied. Objective Cell (Max) Final Value Cell Name Original Value SESI Profit 10800 Variable Cells Final Value Cell Name Original Value Integer SBS2 SCS2 number of units ci 600 Contin number of units c2 700 Contin SDS2 number of units 3 200 Contin Constraints Cell Name Cell Value Formula satus Slack 600 SE$10-SG$10 Binding Binding ŞE$10 Ci minimum SESS Shaper 7200 SESS-SGSS Not SESE Grinder 6300 SES6e-SG56 Binding 300 SEST C3 maimum 200 SEST-SGS7 Binding Not SESE Ci maximum 600 SESB-SGS8 Binding Not Binding 400 SES9 C2 maximum 700 SES9-SG59 300 Microsoft Excel 14.0 Sensitivity Report Worksheet: JAssignment 1 S1 2015-16 solutions.xxQ2 LP formulation MAX Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease SB$2 number of units ci 600 1E-30 1 3 0.666666667 SCS2 number of units 2 700 SD$2 number of units c3 200 1E+30 Constraints Final Shadow Constraint Alowable Allowable Cell Name Value Price RH. Side Increase Decrease 400 85.71428571 SE$10 C1 minimum SESS 600 -1 600 Shaper 7200 1.5 7200 240 2800 SES6 Grinder 6300 6600 1E30 300 C3 maximum C1 maximum SEST 200 200 700 100 SESE 600 1000 1E30 400 SESS C2 maximum 700 1000 1E+30 300

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