Blending Problem Ungoliant Coal co prepares 3 different mixed charcoal (C1, C2, and C3). Each charcoal is made with three types of coal (lignite, antrachite and graphite). The sales price for charcoal C1, C2 and C3 are 35, 30 and 25 dollars and the purchase price per kilogram of lignite, antrachite and graphite are 20, 10 and 5 dollars respectively. Ungoliant co. can purchase up to 30 kilogram of each type of coal. The three types of charcoal differ in their amount of flammability and harmful gas rate. C1 must have an average flammability of at least 10 and contain at most 1% harmful gas. C2 must have an average flammability of at least 8 and contain at most 2% harmful gas rate. C3 must have an flammability of at least 6 and contain at most 1% carbonhydrate. The flammability rates are 15, 8, and 10; and the harmful gas content are 0.5, 2.0, 3.0 for each of the three types coal. It costs $1 to make one sack charcoal due to carrier cut, and Ungoliant can produce up to 140 sacks daily. One sack of charcoal is 1 kg. Ungoliant Coal co. charcoal demand the following amounts of each charcoal: C1: 50 sacks charcoal per day; C2:30 sacks charcoal per day; C3:25 sacks charcoal per day. Ungoliant considers it an obligation to meet these demands. They also has the option of promoting to stimulate demand for its products. Each dollar spent daily in promoting a particular type of charcoal increases the daily demand for that type of charcoal by 1. For example, if Ungoliant decides to spend $10 daily in advertising C22, then the daily demand for C2 will increase by 10*1 = 10 sack of charcoal. Formulate an LP that will enable Ungoliant Coal co' to maximize daily profits. A B C D E F G H L 1 Costs Lignite Antrachite Graphite 20 10 5 15 8 10 Total Profit 0 Flammability Harmful Gas 0.5 2 3 NON ci 50 C2 30 OOOO C3 25 8 o s 140 OV 9 s s 10 30 30 30 11 12 Advert Demand Prices Harmful Gas Const. Flammability Const. 50 13 ci 50 AL 50 14 C2 30 140 120 100 OOO 2 30 ooo 30 15 C3 25 2 25 25 A B F G H J K 1 D E Lignite Antrachite Graphite 20 10 5 15 8 10 2 2. Costs 5 Total Profit 3 0 4 0.5 2 3 5 5 Flammability Harmful Gas c1 C2 C3 0 50 6 0 30 7 0 11 25 00 0 VI 140 9 ov ov 10 30 30 11 12 Advert Demand Prices Flammability Const. Harmful Gas Const. 13 50 140 0 2 50 0 s 50 14 30 C2 C3 120 0 2 30 0 s 30 15 25 100 0 2 25 0 3 25 16 Enter the excel formula that needs to be written in the displayed cell. (add $ symbol if necessary) 114: Hint 1: K14 = 0 Hint 2: in form of Enumber*Cell +/- number cell... (e.g., =-2*A1+3*A2) Correct: 4 pts Incorrect: -6 pts
