Vodafone Ghana is about to make changes to its highly successful and oversubscribed Red monthly call and data plans. It has become necessary that the company cap the number of subscribers due to limited resources, cost reduction plans, and the need to avoid incurring costly penalty for poor customer service (due to oversubscription). There are four different Red plans: Red20, and Red25, Red50, and Red100 at monthly prices of GH20, GH25, GH50, and GH100 respectively. The Red20 and Red25 are targeted at the middle class, whiles the Red50 and Red100 are targeted at the upper class customers. The Red20 offers 200 minutes to call any network (including Vodafone), 500MB of data, and 20 SMS. The Red25 offers 500 minutes to call any network, 125 minutes to call Vodafone numbers only, 1GB of data, and 20 SMS. The Red50 also offers 1000 minutes to call any network, 2GB of data, and 50 SMS. Lastly, the Red100 offers 2000 minutes to call any network, 1000 minutes to call Vodafone numbers only, 5GB of data, and 80 SMS. The companys broadband and SMS contract means that it has up to 40 Million GB of data and 70 Million SMS per month. Also, the companys call contract means it can have a total of 1.2 Billion minutes of calls per month to any network (including Vodafone), and a total of 200 Million minutes of calls to only Vodafone numbers. Per the terms of its contract, when the company exhaust its total minutes of calls to Vodafone only numbers (which it always does), any other calls to Vodafone numbers cost the company the same as calls to any network. Calls to any network cost GH0.01 per minute and the company would want to limit the total cost of calls to any network to GH10 Million per month. Lastly, in order not to lose the middle class market, there must be twice as many Red plans for the middle class as Red plans for the upper class. a. Formulate a linear program to determine the quota for the four different Vodafone Red plans to maximize the companys monthly gross revenue for the Red plans