4. An ofce room of length 60 meters and width 35 meters is to be illuminated by 16 light bulbs of wattage W,, i = 1,. . . , 16. The bulbs are to be located 2 meters above the working surface. Let (12,-, 3),) denote the :1: and y coordinates of the ith bulb. To ensure adequate lighting, illumination is checked at the working surface level at grid points of the form (a, ,6), where 05:10:): p=0313'-'56; OR 4030, Assignment - Ch1 A1_2 6:591, q=0,1,...,7. The illumination at (a, )3) resulting from a bulb of wattage W,- located at (3:5, 39,-) is given by E(a,)) = k mluai) _ triage)" : "(Gui 2) - (its, y,0)||3 where I: is a constant reecting the efciency of the bulb. The total illumination at (oc) is equal to 2,}; Eda, ,6). At each of the points checked, an illumination of between 2.6 and 3.2 units is required. All bulbs have same wattage, say HI, and assume that the wattage 11: may be chosen as any value between 40W and 200W. Formulate a model to decide a minimum wattage w for the 16 bulbs so that the lighting requirement is met. 5. For the above Problem 4, now assume that the wattage w for the 16 bulbs has only four possible choices: 40W, 60W, 100W and 200W. How would you revise the model? 6. Return to Problem 4. Assume it is decided that all bulbs used have the wattage 100W, but we want to use the least number of bulbs to meet the lighting request. It is known that 16 such bulbs are enough, but we wish to use as few bulbs as possible. Give a model to determine how many bulbs are required and where should they be located