The Pro-Shaft Co.

MODELING PROBLEMS I

(Linear Programming)

The Pro-Shaft Co. makes and sells three models or tennis rackets, the Professional (PR), the Extended (EX)  an the Tour (TR). There are two manufacturing processes 1 and 2.  Process 1 has 80 hrs/week available while process 2 has 60. Projected demand for next week for PR+EX combined is no less than 20 and no more than 60. If the profit for each racket is $80 for a  PR, $105 for an EX and $125 for a TR.  Develop an LP model  to find the best production plan for next week!

The Harvest (TH) grows Brocoli and Cauliflower in 500 hectares in the State of Mexico. The  profit from each hectare of brócoli is $150,000 while each hectare of  cauliflower renders $250,000.. Due to demand and company policies no more than 200 hectares of brócoli can be cultivated. During planting season TH has 1200 hrs of labor available. Each hectare of brócoli requires 2.5 hrs of labor to plant whereas each hectare of cauliflower requires  5.5 hrs. Develop an LP model to find the best amount of hectares for each produce. SOLVE THIS PROBLEM USING THE GRAPHIC METHOD ON MILLIMETRIC PAPER

The DeLite Co. makes three loss weigth products Identified as P1, P2 and P3 which use three ingredients which for security reasons we will call Alpha, Beta & Gamma. For each pound of product made quantities in pounds of α, β and γ are consumed according to the table attached. Additionally, other componenets like flavors, colorants, etc are also used.Currently DeLite have 400 lbs of Apha, 800 of Beta and 1000 lbs of Gamma in stock.. If each pound fo P1 contributes  with  $180 to profits.  Each pound of P2 with $120 and  P3 with $150. How many pounds of each product should DeLite.produce to maximize its profits?

Develop an LP MODEL to help the decision makers.

Zohan is a car dealer thar sells cars made by Zircon. Zohan offers three different sizes; compact (CO) médium (MD) and De Luxe (LX)  and two crossovers, Basic (CB) and Luxury (CX) Each vehicle occupies a place either in the exhibition room or the parking area. In total, Zohan has 95 places available at the moment.  Demand for cars is between 50-85 a month of which about 65% are CO and 20% MD. Demand for crossovers is between 10-25 a month, of which about 15% are CX. The profit margin on the selling price is 15%, 25% and 35% respectively on CO, MD and LX cars and of 20% and 40% on CB and CX crossovers respectively. Published prices, in thousands, are CO=$175 MEX, MD=$245 MEX & LX=$375 MEX, while Crossovers sell for CB=$275 MEX and CX=$437 MEX.  How many cars and crossovers should Zohan order from Zircon this month to maximize profits?  Develop the LP MODEL to solve this situation.

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