Sarah Sandoval is a coffee farmer trying to decide how many tons of coffee to produce. She can sell each ton of coffee for $1,500. The cost of producing her first ton of coffee is $300, and the second ton costs $500. Each additional ton of coffee costs $200 more to produce. How many tons of coffee should Sarah produce, and what is the total cost of her coffee production?

Question

Quizplus · Accepted Answer

To determine the optimal production quantity, we need to find the point where the revenue from selling the coffee equals the cost of producing it. Let x be the number of tons of coffee Sarah produces.
Revenue = price per ton * number of tons sold = $1500x
Cost = fixed cost + variable cost = $300 + $500 + ($200 * (x-2)) = $200x + $100
Setting these equal to each other, we get:
$1500x = $200x + $100
Solving for x, we get x = 7. Therefore, Sarah should produce 7 tons of coffee.
To find the total cost of producing 7 tons of coffee, we plug x = 7 into the cost equation:
Cost = $300 + $500 + ($200 * (7-2)) = $6300
Therefore, the best choice is B; she will produce seven tons at a total cost of $6,300.

Sarah Sandoval Is a Coffee Farmer Trying to Decide How