# Costs and Decision Models

Lecture 2

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Shelby Shelving Decision Model Decision Models Decision Variables: Let S = # of Model S shelves to produce, and LX = # of Model LX shelves to produce. To specify the objective function, we need to be Lecture 2 Shelby Shelving Case Understanding the optimizer sensitivity report ! Dual prices ! Righthand side ranges ! Objective coefﬁcient ranges If time permits: Distribution / Network Optimization Models Summary and Preparation for next class LX ) Net proﬁt 39S 55LX 400 and 1 So for the current production plan of S 1400, we get Net proﬁt = $61,400. Selling Price Standard cost Proﬁt contribution able to compute net proﬁt for any production plan S; LX . Case information: S 1800 1839 39 LX 2100 2045 55

Is equation (1) correct?

Decision Models:

Lecture 2

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Decision Models:

Lecture 2

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Equation (1) is not correct (although it does give the correct net proﬁt for the current production plan). Why? Because the standard costs are based on the current production plan and they do not correctly account for the ﬁxed costs for different production plans. For example, what is the net proﬁt for the production plan S Net proﬁt LX 0? Since Variable cost Fixed cost 385,000. max subject to: Revenue

Shelby Shelving LP Decision Variables: Let S = # of Model S shelves to produce, and LX = # of Model LX shelves to produce. Shelby Shelving Linear Program 260 S 245 LX 385;000 (Net Proﬁt) (S assembly) (LX assembly) (Stamping) (Nonnegativity) 0:3 S (Forming) 0:25 S S LX 0:3 LX 0:5 LX S; LX 1900 1400 800 800 0

and Fixed cost = 385,000, the Net proﬁt is But equation (1) incorrectly gives Net proﬁt 39S 55LX 0

To derive a correct formula for net proﬁt, we must separate the ﬁxed and variable costs. Proﬁt Contribution Calculation Model S Model LX a) Selling price 1800 2100 b) Direct materials 1000 1200 c) Direct labor 175 210 d) Variable overhead 365 445 e) Proﬁt contribution 260 245 (e = a b c d) The correct objective function...

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