A factory produces two products, A and B. The production of x barrels of A and y barrels of B results in CO…

Question

A factory produces two products, A and B. The production of x barrels of A and y barrels of B results in CO emissions of 0.25x + 0.60y units and SO2 emissions of 0.60x + 0.20y units. The factory's dai

ScanSolve AI Tutor · Accepted Answer

The system of inequalities for Q2 shown in your work is correct.

Q2: System of Inequality
The system of inequalities is:

0.25x + 0.60y \le 75

0.60x + 0.20y \le 90

x \ge 0

y \ge 0

Q3: Would it be legal for the factory to produce 100 barrels of A and 80 barrels of B per day?

Substitute $x = 100$ and $y = 80$ into the CO emission inequality.
$0.25(100) + 0.60(80) \le 75$ $25 + 48 \le 75$ $73 \le 75$
This condition is satisfied.
Substitute $x = 100$ and $y = 80$ into the SO₂ emission inequality.
$0.60(100) + 0.20(80) \le 90$ $60 + 16 \le 90$ $76 \le 90$
This condition is also satisfied.

Since both emission limits are met, it would be legal.
The answer is: $\boxed{\text{Yes, it would be legal.}}$

Q4: Would it be legal for the factory to produce 60 barrels of A and 160 barrels of B per day?
Substitute $x = 60$ and $y = 160$ into the CO emission inequality.
$0.25(60) + 0.60(160) \le 75$ $15 + 96 \le 75$ $111 \le 75$
This condition is not satisfied, as 111 is greater than 75.
Substitute $x = 60$ and $y = 160$ into the SO₂ emission inequality.
$0.60(60) + 0.20(160) \le 90$ $36 + 32 \le 90$ $68 \le 90$
This condition is satisfied.

Since the CO emission limit is exceeded, it would not be legal.
The answer is: $\boxed{\text{No, it would not be legal.}}$

A factory produces two products, A and B. The production of x barrels of A and y barrels of B results in CO emissions of 0.25x + 0.60y units and SO2 emissions of 0.60x + 0.20y units. The factory's dai

Step-by-step solution

Substitute $x = 100$ and $y = 80$ into the CO emission inequality.

Substitute $x = 100$ and $y = 80$ into the SO₂ emission inequality.

Substitute $x = 60$ and $y = 160$ into the CO emission inequality.

Substitute $x = 60$ and $y = 160$ into the SO₂ emission inequality.

Still stuck on this one?

More Mathematics Questions

A factory produces two products, A and B. The production of x barrels of A and y barrels of B results in CO emissions of 0.25x + 0.60y units and SO2 emissions of 0.60x + 0.20y units. The factory's dai

Step-by-step solution

Substitute x=100x = 100x=100 and y=80y = 80y=80 into the CO emission inequality.

Substitute x=100x = 100x=100 and y=80y = 80y=80 into the SO₂ emission inequality.

Substitute x=60x = 60x=60 and y=160y = 160y=160 into the CO emission inequality.

Substitute x=60x = 60x=60 and y=160y = 160y=160 into the SO₂ emission inequality.

Still stuck on this one?

More Mathematics Questions

Substitute $x = 100$ and $y = 80$ into the CO emission inequality.

Substitute $x = 100$ and $y = 80$ into the SO₂ emission inequality.

Substitute $x = 60$ and $y = 160$ into the CO emission inequality.

Substitute $x = 60$ and $y = 160$ into the SO₂ emission inequality.