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Info3010, Week 5 notes

by: Rebecca Evans

Info3010, Week 5 notes Info3010

Marketplace > Tulane University > Business > Info3010 > Info3010 Week 5 notes
Rebecca Evans
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These notes cover the material from class on February 10th and 12th and include detailed instructions on different excel functions.
Business Modeling
Srinivas Krishnamoorthy
Class Notes
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This 4 page Class Notes was uploaded by Rebecca Evans on Friday February 12, 2016. The Class Notes belongs to Info3010 at Tulane University taught by Srinivas Krishnamoorthy in Spring 2016. Since its upload, it has received 19 views. For similar materials see Business Modeling in Business at Tulane University.

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Date Created: 02/12/16
Notes from class on February 10th Dorian Auto   Dorian Auto is considering manufacturing three types of cars (compact, midsize, and large)  and two types of minivans (midsize and large). The resources required and the profit  contributions yielded by each type of vehicle are shown in the table below. At present, 6500 tons of steel and 65,000 hours of labor are available. If any vehicles of a given type are produced then production of that type of vehicle is economically feasible only if at least a minimal number of  that type are produced. These minimal numbers are also listed in the table below. Dorian wants  to find a production plan that maximizes its profit.    Compact car  Midsize car  Large car  Midsize  Large  Minivan  Minivan  Steel  1.5  3  5  6  8  (tons/unit)  Labor  30  25  40  45  55  (hours/unit)  Minimum  1000  1000  1000  200  200  production (if any)  Profit  $2,000  $2,500  $3,000  $5,500  $7,000  contribution    Conceptual Formulation 1 Decision Variable: a Which cars/minivans to produce and in what quantities?  i Y 11 if compact cars are produced, Y =0, 1therwise ii Y 51, if large minivans are produced, =0 otherwise (binary) iii X 1# units of compact cars produced iv X =2 units of large minivans produced (numerical) 2 Objective a Maximize total profit  b Total Profit=2,000X  1 2,500 X  +23,000X + 3 500X + 7,4 0X 5 i Don’t multiply by Y variable because then non­linear  3 Constraints  a Threshold production level constraint  i 1,000Y  ≤1X ≤ 1 000,000Y 1 1 Explanation: lower limit=1,000Y and 1 per limit= 1,000,00   1  (artificial upper limit­large number that doesn’t matter, can write  infinity) 2 Suppose Y =01then 0 ≤ X ≤ 01  3 Suppose Y =11then 1,000 ≤ X ≤ 1,1 0,000 ii 200Y  5 X ≤5 ,000,000Y for5 arge minivans b Resource constraints i Labor constraint: 30X  + 25X  + … + 55X  ≤ 6,500 hours 1 2 5 ii Steel constraint: 1.5X  1 3X  2 … + 8X ≤ 65 00 tons of steel c Binary constraint: Y ,1Y ,2…Y  a5e binary Excel 4 Total profit is =sumproduct(units produced, contribution per unit) 5 Constraints a Resource constraints are =sumproduct(units produced, steel or labor hours per  unit) b Units produced rowlink to decision units produced row c Lower limit(min. production) =minimum production*binary variable  d Upper limit on production = 1,000,000 (or any large number) * binary variable 6 Solver a Objective: C17 (total profit cell) b Max c By changing variable cell: decision cells=produce? And units produced (Y and X  variables conceptually) d Constraints i Steel and labor hours cells ≤ Resource available cells ii Minimum production row ≤ units produced iii Units produced ≤ upper limit on production iv Binary constraint: produce? Decision row is “bin” (binary)  e No option for sensitivity report because using binary variables  th  Notes from class on February 12  The Javitz club in New York City has one jazz performance every weeknight (Mon to Thu). The expected ticket demand for weeknight performances is given by the relationship below:  Demand = 333 – 3.33 × price The capacity of the club is 200 seats.  1) What is the optimal weeknight price that the club should charge? Non­linear optimization model: most pricing problems are non­linear Conceptual formulation 1. Decision Variable a. What price to charge for weeknight tickets? (p=price)  2. Objective a. Maximize revenue b. Revenue= p*q = price * quantity sold at price p c. Quantity demanded @ price= 333­3.33 x price d. Revenue= p*(333 – 3.33 × price) e. =333p – 3.33p 2 i. Non­linear because p is squared 3. Graph Q    Price Slope= ­3.33 and y­intercept= 333 4. Constraint a. Capacity constraint i. Q ≤ 200 ii. 333 – 3.33 × price ≤ 200 b. Non­negativity constraint i. P ≥ 0 Excel 1. Solver a. Objective: revenue cell b. Changing cell: price c. Constraint: tickets sold ≤ capacity (200 tickets) d. ***Choose solving method: GRG non­linear  Results  Solution: choose a price where demand is below capacitymaximize revenue is goal (not filling to capacity)   Advantage of more people: club sells other goods/service (drinks)higher secondary  revenue (not take into account)  In future modeling: goal programing=can have 2 objectives  Review of Course this far: Modeling cycle Business situation”modeling step” conceptual formulation    spreadsheet  modelinsightsmanagerial insights     Modeling world and real world  Deterministic Model Application  Production and transport  Marketing and advertising   Finance and investing linear Continuous linear programs optimization Integer/binary programs Nonlinear programs Mixed programs 


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