# MAKEUP MIDTERM-2

```MATH 224 MIDTERM MAKEUP
SPRING 2019/20
DUE: 18/6/2020 14:00
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
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You need to show every step of your calculations and you need to write explanations as
required.
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I want to remind you that this is an individual work. You cannot share your work with
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)
```