Mr. Cutler should make 2 bricks and 7 tiles to maximize his profit.
<u>Step-by-step explanation:</u>
Let the no. of bricks be 'b'
Let the no. of tiles be 't'
Time taken for 1 brick = 10 mins
Time taken for 1 tile = 20 mins
Clay used for 1 bick = 3 pounds
Clay used for 1 tile = 2 pounds
Profit on each brick = $2
Profit on each tile = $3
Total time available= 160 mins
Total clay available = 20 pounds
10b + 20t = 160
b + 2t = 16
b = 16 - 2t
3b + 2t = 20
3(16 - 2t) +2t = 20
48 - 6t + 2t = 20
48 - 4t = 20
-4t = 20-48
4t = 28
t = 7
b = 16 - 2t
b = 16 - 14
b = 2
Mr. Cutler should make 2 bricks and 7 tiles to maximize his profit.
Let x and y be the dimension of the rectangle. Suppose x is the width and y is the length. Since the perimeter is 36, we have
![2(x+y)=36 \iff x+y=18 \iff y = 18-x](https://tex.z-dn.net/?f=%202%28x%2By%29%3D36%20%5Ciff%20x%2By%3D18%20%5Ciff%20y%20%3D%2018-x%20)
If we increase the length by 1, we change
. Similarly, if the width is increased by 2, we change
. So, the increased area is
![(x+2)(y+1)=30](https://tex.z-dn.net/?f=%20%28x%2B2%29%28y%2B1%29%3D30%20)
If we substitute the value for y deduced in the first equation, we have
![(x+2)(18-x+1)=30 \iff (x+2)(19-x) = 30 \iff -x^2+17x+38 = 30 \iff x^2-17x-8=0](https://tex.z-dn.net/?f=%20%28x%2B2%29%2818-x%2B1%29%3D30%20%5Ciff%20%28x%2B2%29%2819-x%29%20%3D%2030%20%5Ciff%20-x%5E2%2B17x%2B38%20%3D%2030%20%5Ciff%20x%5E2-17x-8%3D0)
The solutions to this equation are
![\dfrac{17\pm\sqrt{321}}{2}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B17%5Cpm%5Csqrt%7B321%7D%7D%7B2%7D%20)
One of them is negative, so we have to choose the positive one:
![x=\dfrac{17+\sqrt{321}}{2}](https://tex.z-dn.net/?f=%20x%3D%5Cdfrac%7B17%2B%5Csqrt%7B321%7D%7D%7B2%7D%20)
Which implies
![y = 18 - \dfrac{17+\sqrt{321}}{2} = \dfrac{19-\sqrt{321}}{2}](https://tex.z-dn.net/?f=%20y%20%3D%2018%20-%20%5Cdfrac%7B17%2B%5Csqrt%7B321%7D%7D%7B2%7D%20%3D%20%5Cdfrac%7B19-%5Csqrt%7B321%7D%7D%7B2%7D%20)
I think it’s just 68% ? But I might be wrong, sorry.
Answer: 22 hours 28 minutes
Step-by-step explanation: 0843 means 8:43am and 0711 means 7:11am military time. In that order there is 22 hours 28 minutes from 8:43am today to 7:11 am tomorrow. The question itself is rather confusing so if this is not what you meant please let me know and I will re-do it.