Question

A surfboard shaper has to limit the cost of development and production to ​$288 per surfboard. He has already spent ​$61,466.00 on equipment for the boards. The development and production costs are ​$142 per board. The cost per board is 142x /x+ 61,466 /x dollars. Determine the number of boards that must be sold to limit the final cost per board to $ 288.


How many boards must be sold to limit the cost per board to​$288?

Answer 1

Answer:

At least 421 units of boards need to be sold to limit the cost per board to $288

Step-by-step explanation:

Let the number of surfboards made or sold be x

Total cost = fixed cost + variable cost

Fixed Cost = $61466

Variable Cost = 142 × x = $142x

Total cost = 61466 + 142x

Revenue = unit price × quantity = 288×x = 288x

The number of boards that needs to be sold to limit the cost off a board to $288 is the number of units at the point where the total cost matches the revenue.

61466 + 142x = 288x

288x - 142x = 61466

146x = 61466

x = 421 units.