Problem 3. (30 points, 2 each part) Answer this problem on this sheet using the spaces indicated. Answer the following questions regarding the following primal model using the solution and analysis of sensitivity obtained with Excel Solver which is on the next page. X1 = Number of apple trees to plant X2 = Number of avocado trees to plant Max Z = 5000X1 + 7000X2 (Total profit) subject to 20X1 + 10X2  1000 (Fertilizer available in Ton) 2X1 + 3X2  200 (Hectares of land available) X1 + 2X2  2400 (Available man hours) 25X1 + 50X2  35000 (Liters of water available) 10X1 + 15X2  15000 (Budget available) X1, X2  0

How many trees of each type must be planted? ___________________________________________ 2. What is the utility with this combination? _________________________________________________ 3. Will the company exhaust all its resources? Which yes and which no? Of those that remain available, how many units are left of each? _____________________________________________________________ ___________________________________________________________________________________________ ___________________________________________________________________________________________ ______________________________________________________________________ 4. They want to buy 100 tons of fertilizer from the company at 50 per ton; Should you sell it? By that?______________________________________________________________________________ ___________________________________________________________________________________________ _________________________________________________________________________________ 5. If the utility generated by each apple tree increases from 5000 to 10,000 and the utility generated by each avocado tree, do the optimal values of the decision variables change? _________ 6. If the profit generated by each avocado tree decreases from 7000 to 2000 and the profit generated by each apple tree, do the optimal values of the decision variables change? _________ 7. If the available fertilizer increases from 1000 to 1010, then the total profit increases by 250. Check the box correct answer: True_______ False_______

8. If the number of hectares is reduced to 199, the optimal total utility is _______________________________. 

Problema 3. (30 puntos, 2 cada inciso) Conteste este problema en esta hoja utilizando los espacios indicados. Contestar las siguientes preguntas con respecto al siguiente modelo primal utilizando la solucin y anlisis de sensibilidad obtenidos con Solver de Excel la cual est en la siguiente pgina. X1 = Nmero de rboles de manzana a plantar X2 = Nmero de rboles de aguacate a plantar (Utilidad total) Max Z= 5000X1 + 7000X2 sujeto a 20X1 + 10X2 0 (Fertilizante disponible en Ton) (Hectreas de tierra disponibles) (Horas hombre disponibles) (Litros de agua disponibles) (Presupuesto disponible) Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $A$2 X1 25 0 5000 9000 333.333333 $B$2 X2 50 0 7000 500 4500 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $C$7 Max 2 = 1000 25 1000 1000 333.333333 $C$8 Max Z= 200 2250 200 100 100 $C$9 Max 2 = 125 0 2400 1E+30 2275 $C$10 Max 2 = 3125 0 35000 1E+30 31875 $C$11 Max 2 = 1000 0 15000 1E+30 14000