Question

Please write out the 3 that apply.

[47500] Question 6 Select the three correct statements below. Three companies have purchased the pre-diabetes medication. The orders from each company a represented in matrix X: Select 3 that apply. • The first column indicates how many bottles of pill A a company purchases. • The second column indicates how many bottles of pill B a company purchases. • The third column indicates the presence of a fixed cost. The fixed overhead charge is $5,000. The total cost for each company is represented by matrix Z. One bottle of Pill B costs $35. fixed X= Pill A 1000 800 1500 Pill B 800 1000 500 1 1 One bottle of Pill B costs $25. One bottle of Pill A costs $15. Z= [45000 46000 47500 One bottle of Pill A costs $20. Select the three correct statements below. The fixed overhead charge is $7,500. Select 3 that apply.

Answer 1

Let
a = price of one pill A, b= Price of one pill B
and
C= fixed overhead charges

Then we have to solve the system

${\bf X}{\bf b}={\bf z}$ Where X and Z are as given. And

b b L

The augmented matrix for teh above system is

$[ {\bf X} : {\bf z}]= \begin{bmatrix} 1000& 800 &1 &:& 45000\\ 800& 1000& 1&:& 46000 \\ 1500 & 500& 1&:& 47500\end{bmatrix} \\ ~~~~~~~~~~~~\sim \begin{bmatrix} 1000& 800 &1 &:& 45000\\ -200& 200& 0&:& 1000 \\ 500 & -300& 0&:& 2500\end{bmatrix}$

By applying the transformation

Now again apply the transformation $R_3=R_3+{3\over 2}R_2$ we get

$[ {\bf X} : {\bf z}]\sim \begin{bmatrix} 1000& 800 &1 &:& 45000\\ -200& 200& 0&:& 1000 \\ 200 & 0& 0&:& 4000\end{bmatrix}$ ---------------(1)

From the last row we get

$200a=4000 \\ \Rightarrow a=20$

So Price of one pill A is $20

From the 2nd row of (1) we get

$-200(20)+200b=1000 \\ \Rightarrow b=25$

So Price of one pill B is $25

Similarly from row 1st of (1) we get

$c=5000$

So the fixed overhead charges are $5000

Hence the correct Options are First, Third and Fifth