MATH 224 MIDTERM MAKEUP SPRING 2019/20 DUE: 18/6/2020 14:00 How to submit your exam You can submit this homework using Microsoft word (preferred), or scan of your handwritten answers as one single pdf file. You CANNOT submit single pictures of the pages that you wrote to answer these questions. Submissions in the form of pictures WILL NOT BE GRADED. You can find free scanning applications for your cell phones to scan your pages, you don’t need a scanner device. Using Microsoft Word does not mean inserting pictures on word you need to type your answers. How to answer the questions - You need to show every step of your calculations and you need to write explanations as required. - I want to remind you that this is an individual work. You cannot share your work with others and ask questions to your instructor about the exam during this period. WHO CAN SUBMIT THIS EXAM Students who didn’t submit any homework or quiz before the final assignment can submit QUESTIONS 1- Use bisection method to find root of the equation sin(3x)+5x-3. Show every single step in your procedure. Percent relative error needs to be less than 0.5% (50p) 2- A chemical plant is producing two types of products ; Product A and Product B. These two products are produced by using same two raw materials (raw material: a chemical that is used to produce another chemical) Raw1 and Raw2. In order to produce 1 ton of ProductA you need to spend 2 tons of Raw 1 and 2 tons of Raw2 similarly in order to produce 1 ton of ProductB you need to spend 3 tons of Raw1 and 4 tons of Raw2. Other details about the production for a week is given in the table below: Raw1 Raw2 Time Storage Selling Price ProductA 2tons/tonA 2tons/tonsA 5h/tonsA 15tons 60$/tonA ProductB 3tons/tonB 4tons/tonB 2h/tonB 40tons 100$/tonB Availability 100 tons 100 tons 90 hours Cost of Raw1 and Raw 2 are both 10$/ton. Use linear programing along with graphical method to find out maximum profit that can be obtained by this chemical plant. How much ProductA and ProductB is required to obtain this profit. (you cannot use optimization tools you need to apply graphical method). (50p)