Sal\'s Sunglass Hut Consider the following sensitivity report for Sal\'s Sunglas

Question

Sal's Sunglass Hut Consider the following sensitivity report for Sal's Sunglass Hut, which makes two models of sunglasses (deluxe and standard). Sal has up to 440 hours of available labor next month. He has scheduled 300 for shipping, 120 for production and 20 hours for advertising. The following solution is based on maximizing profit. Final Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 7.5 3.5 Name Value D (Deluxe) S (Standard) 450 50 1.00E+30 800 25 10 Shadow Constraint Allowable Allowable Price R.H. Side Increase Decrease 53..5 40 4.2 Final Name Value Shipping Production Advertising minimum 260 120 20 300 1.00E+30 32 10 1.5 120 2.6 20 a. Identify the decision variables, objective function, and constraints in simple verbal statements. b. Mathematically formulate a linear optimization model.

Explanation / Answer

a) Decision variables are production mix of the two models - Deluxe and Standard.

Objective function is profit maximization. Total Profit is equal to 50 contribution by Deluxe and 25 contribution by Standard

There are four resource constraints - There are total of 440 labor hours out of which 300 hours are available for shipping, 120 hours for production and 20 hours for advertising.

b) Mathematical formulation of linear optimization model is as under:

Let D and S be the number of Deluxe and Standard models to be produced

Max 50D+25S

requirement of each resource (i.e. how much shipping hours, production hours, advtg hours etc required per unit for each model) in production of the two models is not specified in the question. Therefore, constraints cannot be formulated mathematically. We only know the resource availability, which makes the right hand side of the constraint inequalities.

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