The company Goggles has developed a platform for offering cloud services. It has made a shortlist of 20 services (S1 up to $20) to offer, as shown in the table below Service $1 S2 S3 $4 S5 S6 S7 S8 $9 $10 $11 $12 $13 $14 $15 $16 $17 $18 $19 $20 Category Finance Finance Leisure Business Sports Games Business Sports Sports Finance Games Leisure Sports Business Games Games Business Business Sports Finance Size (GB) Memory (GB/slot) CPU (s/slot) Expected users 114 49 98 106 130 123 143 45 128 14 131 55 41 7 33 31 89 36 134 133 61 80 182 79 277 311 382 260 135 327 58 360 138 102 345 237 188 128 225 206 5 438580 18 10mm50016H35 10 94 93 55 10 103 90 80 44 87 880 1930 10780 7410 12710 13480 1270 4530 11060 780 10630 1550 12070 13080 11370 1810 11050 5720 2810 8150 Each service has an associated category, size in GB, memory requirement (in GB per slot), CPU re- quirement (in seconds per slot), and expected number of users. The memory and CPU requirements are calculated relative to a specific fixed slot size (time unit). In total, there is 900GB storage available (size), and there is 2500GB memory and 600 seconds of CPU available per slot. Goggles wants to determine which services to offer so that the total available storage, memory, and CPU limits are not exceeded, while maximizing the total expected number of users. Each service can be offered at most once, and we cannot offer services in fractional amounts. We will model and solve this problem using integer linear programming. 1. What are the variables for this model? 2. What is the objective function? 3. Write down the constraints that ensure that the total available storage, memory, and CPU limits are not exceeded. 5. Because of the nature of services in different categories, Goggles needs to adhere to the following additional requirements as well: We cannot offer all of the services in the Leisure category simultaneously. The services in the Games category have the following particular requirement. Service $15 can be offered only if service $16 is offered. We can offer the Sports category service $5 only if service S8 is not offered and service $9 is offered. We would like to offer at least three services in the Business category. (a) Write down the constraints that ensure each of these requirements on the categories. (b) Implement and solve integer linear programming model which includes these additional con- straints from part (a) in Excel, and generate the Answer Report. (Remember to solve your model as an LP by selecting Simplex LP as the solver engine, and do not forget to set the integer optimality tolerance level to 0% in the Solver options.) What is the optimal objective value?