6. A hotel has 120 empty rooms which will be furnished into Regular and Deluxe rooms, both with same sizes. Construction for Regular and Deluxe rooms cost 2 275,000 and P 400,000 each, respectively. A budget of ? 40,000,000 is allotted in constructing the hotel rooms. If the hotel management plans to charge P 3,500 per night for Regular rooms and P5,500 per night for Deluxe rooms, how many Regular and Deluxe rooms should be constructed so that the revenue from accommodations during a fully-booked night is maximized? The problem above is a linear programming problem. Each item below would be a step-by-step guide for you to answer this. Follow them and you should be able to answer this easily. (a) The values of interest in this problem are the number of Regular and Deluxe rooms. Define these as your variables. (b) Identify what you want to minimize/maximize. Write an expression for it in terms of your variables. (c) A constraint in the problem is the number of rooms in the hotel. Write an inequality that describes this constraint. (Why inequality? Do we have to furnish all rooms?) (d) Another constraint in the problem is the cost of construction for the rooms. Write an inequality that describes this constraint. (e) Is there a limit to the number of Regular and Deluxe rooms in the hotel? If so, write inequalities for the lower and upper bounds of the variables. (f) Your answers in (a) to (e) forms part of the linear programming model. The expression in (b) is the objective function and the inequalities in (c) to (e) are the constraints of the problem. Graph (c) to (e) and identify the feasible region: the region at which ALL constraints are satisfied. Label all the vertices of your feasible region. You may use any calculator (physical or online) to identify the intersection of your lines. (g) The Fundamental Theorem of Linear Programming states that the optimal values occur at the vertices of the feasible region. Identify the vertices of your feasible region and identify the value of the objective function in (b) for each vertex. (h) The vertex in (g) that produced the best (lowest or highest, depending on whether you want to minimize or maximize) objective function value is the answer to the problem. What does this mean about the optimal number of Regular and Deluxe rooms for the hotel? This hint can be used (a) Let r be the number of regular rooms and d be the number of Deluxe rooms. (b) We want to maximize revenue .Recall that revenue=(price)(quantity sold) (c) How many rooms do we construct (in terms of r and d) ? Do we have to furnish all rooms? (d) Recall that total cost= (individual cost)(quantity produced). Is there a maximum amount in our spending ? e) Can we construct 50 rooms of one kind? How about 120? 170? - 20? For (f) to (g), please check our class notes on LineaProgramming. You may also check the solution to the example discussed in classx, which I have written in the next page of this document. 1. maximize z = Fx+sy, subject to x2 0, yzD, 2x+Sy