Problems 1. DynaTune is trying to determine how to allocate its $145,000 advertising budget for a new product. Radio and television are the two media outlets selected for advertising. The following table shows the costs of advertising in these two media and the estimated number of new customers reached by increasing amounts of advertising Media Type & Number of Ads Number New Customers Cost per Reached Ad Radio 1-10 900 $1000 Radio 11-20 700 $900 Radio 21-30 400 $800 Television 1-5 10,000 $12,000 Television 6-10 7500 $10,000 $8000 Television 11-15 5000 For example, each of the first 10 ads the company places on the radio will cost $1000 and is expected to reach 900 new customers. Each of the next 10 will cost $900 and is expected to reach 700 new customers. Assume the company will purchase no more than 30 radio ads and no more than 15 television ads. a. Formulate an LP to maximize the number of new customers reached. 2. Montana Pulp (MP) produces recycled paperboard by combining four grades of recycled paper stock. Each grade of stock has a different strength, color, and texture. The strength, color, and texture of the finished paperboard are a weighted average of those characteristics of the paper stock inputs. The table provides the characteristics of the paper inputs and their costs per ton. An order for 500 tons of paperboard with a strength of at least 7, a color of at least 5, and a texture of at least 6 has been received. MP needs to find the minimal-cost mix of inputs required to satisfy this order. 1 Paper Stock Strength Color Texture Cost/Ton 8 9 8 $150 6 7 5 $110 3 5 5 6 $90 4 3 4 5 $50 2 a. Formulate an LP to minimize the cost of the order