Activity 1. Getting acquainted with the essential terms and concepts of operations research, what also matters is you should also be able to apply these concepts in solving problems. Solve the following problems graphically. 1. Royal Co. manufactures aluminum sheets and aluminum bars. The maximum production capacity is estimated at either 800 sheets or 600 bars per day. The maximum daily demand is 550 sheets and 580 bars. The profit per ton is 40 per sheet and 35 per bar. Determine the optimal daily production mix. 2. In the Save Mart grocery store, shelf space is limited and must be used effectively to increase profit. Two cereal items, Oatie and Wheatie, compete for a total shelf space of 60 ft2 . A box of Oatie occupies 0.2 ft2 and a box of Wheatie needs 0.4 ft2 . The maximum daily demands of Oatie and Wheatie are 200 and 120 boxes, respectively. A box of Oatie nets 1.00 in profit and a box of Wheatie 1.35. Save Mart thinks that because the unit profit of Wheatie is 35% higher than that of Oatie, Wheatie should be allocated 35% more space than Grano, which amounts to allocating about 57% to Wheatie and 43% to Oatie. What do you think? 3. Fuji Motorcycles can advertise its products on local radio and television (TV). The advertising budget is limited to 10,000 a month. Each minute of radio advertising costs 15 and each minute of TV commercials 300. Show & Sell likes to advertise on radio at least twice as much as on TV. In the meantime, it is not practical to use more than 400 minutes of radio advertising a month. From past experience, advertising on TV is estimated to be 25 times as effective as on radio. Determine the optimum allocation of the budget to radio and TV advertising. 4. A furniture company manufactures desks and chairs. The sawing department cuts the lumber for both products, which is then sent to separate assembly departments. Assembled items are sent for finishing to the painting department. The daily capacity of the sawing department is 200 chairs or 80 desks. The chair assembly department can produce 120 chairs daily and the desk assembly department 60 desks daily. The paint department has a daily capacity of either 150 chairs or 110 desks. Given that the profit per chair is 50 and that of a desk is 100, determine the optimal production mix for the company