Your entrepreneurial uncle Joe is running a lawn sign business. Joe manufactures the following three types of lawn signs: Political Party signs (PP) Environmental Consciousness signs (EC) Other Woke signs (OW) To help Joe sell his products you decided to develop a new online ad placement strategy. Currently, the following channels offer to host ads at the following base price: Facebook (F): at most 5000 ads at 35 cents per impression Instagram (I): at most 5000 ads at 40 cents per impression Tiktok (T): at most 5000 ads at 50 cents per impression Additionally, Facebook has a surcharge of 10 cents per impression for political ads, which would apply to PP but not to EC or OW. a) Draw a network diagram to represent the problem. You can either draw the diagram by hand and take a picture of your drawing, or use Word/PPT. Indicate the decision variables on the diagram. b) If Joe has a budget of $5K for this fall's advertising campaign, how should he allocate ads to channels to generate the greatest number of impressions? c) If Joe decides to advertise on Tiktok, he will need to hire someone to produce ads (since Tiktok ads run in video format). Your friend Silvia offered to help with the production of ads for Tiktok for a fee of 20 cents per impression. You can assume that ads for other channels can be produced at no cost. How would this change your solution from b)? d) Market research has shown that political party ads (PP) are not particularly interesting for Tiktok users. In particular, the clickthrough rate on PP is half of the rate for OW types of ads. In contrast, the clickthrough rate for environmental consciousness ads (EC) is double the OW ads on Tiktok. All clickthrough rates on the remaining channels (F and I) are equal to OW rates on Tiktok. How should Joe spend $5K to maximize the number of clicks on his ads? Assume the costs from part c).