What is the linear model for the profit of selling Glug. How much would they make if they sold 80 barrels in one day?

Question

In one day, the concession stands at a Podracing venue on Malastare can sell 20 barrels of Glug at a profit of 3000 credits and 50 barrels of Glug for a profit of 9000 credits. Write a linear model for the profit of selling Glug. How much would they make if they sold 80 barrels in one day?

Answer 1

The linear equation has the form P=aQ+b where P is the profit in credits and Q is the quantity or number of barrels of Glug. The slope “a” is (9000-3000)/(50-20)=6000/30=200 credits per barrel.

We can write P-3000=200(Q-20), P=200Q-4000+3000=200Q-1000. So the profit P(Q)=200Q-1000.

When Q=80 barrels, P(80)=200×80-1000=15000 credits.