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5A company produces two products, A and B, using machine hours and labor hours. Each unit of Product A requires 3 machine hours and 2 labor hours, while each unit of Product B requires 2 machine hours and 4 labor hours. The company has 180 machine hours and 240 labor hours available per day. If the profit per unit is $10 for Product A and $15 for Product B, how many units of Product B should be produced to maximize profit?
Let x = units of Product A, y = units of Product B.
Solving the system graphically or via corner point analysis:
Now plug y = 45 into x = 120 - 2(45) = 30
Check profit: P = 10(30) + 15(45) = 300 + 675 = 975
P = 10(28) + 15(46) = 280 + 690 = 970 < 975
Thus, to maximize profit, the company should produce 45 units of Product B.
A science communicator films a video explaining exponential decay in radioactive isotopes. The half-life of a certain isotope is 8 days. If the initial sample has a mass of 200 grams, how many grams will remain after 24 days?