1 TRq 16q2 1000q TC q 26q 3484 What selling price leads

1.) TR(q) = -16q^2 + 1000q

TC (q) = 26q + 3484

What selling price leads to the largest possible profit?

2.) For what Quantity is average cost exactly $243.75 per Trinket?

Solution

1).

Revenue function, TR (q) = -16q^2+1000q

Total cost function TC (q) = 26q+3484

Profit= Revnue- cost= -16q^2 + 974q-3484

Break even point, where revenue= cost

It means profit is 0.

-16q^2 + 974q - 3484 = 0

Root of the equation is = 3.81, 57

rounding off 3.81= 4

if company produce the item bet 4 to 57, company will earn profit.

Max value of function occur, when company will sell 30 item (by using the maxima and minima condition)

Total revenue for 30 item TR (30) = 15600

Selling price for maximum profit= TR (30)/30= $520

2).

Average cost= TR(q)/q= (-16q+1000)q/q

243.75 = -16q+1000

q= 47.26~ 47 units