Break Even Point / Market Equilibrium Point Problems

[currypuff]

1.) A calculator manufacturer's total cost function is C(x) = 25x + 2025. The total revenue function is linear and the total revenue for 100 calculators is $7000 while the total revenue for 150 calculators is $10,500. Find the break-even point.

2.) A retailer will buy 200 videos from the wholesaler if the price is $10 each and will buy 150 videos if the price is $15 each. The wholesaler is willing to supply 100 videos at $8 each and 150 videos at $10 each. Assuming the supply and demand functions are linear, find the market equilibrium point.

Thanks in advance for your assistance.

 

[Deleted member 4993]

1.) A calculator manufacturer's total cost function is C(x) = 25x + 2025. The total revenue function is linear and the total revenue for 100 calculators is $7000 while the total revenue for 150 calculators is $10,500. Find the break-even point.

2.) A retailer will buy 200 videos from the wholesaler if the price is $10 each and will buy 150 videos if the price is $15 each. The wholesaler is willing to supply 100 videos at $8 each and 150 videos at $10 each. Assuming the supply and demand functions are linear, find the market equilibrium point.

Thanks in advance for your assistance.

Please show us your work - and exactly where you are stuck - so that we know where to begin to help.

 

[stapel]

To help you get started....

1.) A calculator manufacturer's total cost function is C(x) = 25x + 2025. The total revenue function is linear and the total revenue for 100 calculators is $7000 while the total revenue for 150 calculators is $10,500. Find the break-even point.

They've given you two data points for the revenue function: for x units and R dollars of revenue, you have (x, R) = (100, 7000) and (x, R) = (150, 10500). Using these two points, find the equation of the straight line which models the revenue. Then review the definition of the "break-even" point to figure out the equation you need to solve. :idea:

2.) A retailer will buy 200 videos from the wholesaler if the price is $10 each and will buy 150 videos if the price is $15 each. The wholesaler is willing to supply 100 videos at $8 each and 150 videos at $10 each. Assuming the supply and demand functions are linear, find the market equilibrium point.

It is my understanding that, in the study of economics, finding the market equilibrium point involves partial differential equations. But I don't think you're to that point yet...? :?:

Please provide the definitions and/or formulas you're supposed to be using for this. When you reply, please include a clear listing of everything you have tried so far. Thank you!

Eliz.