to produce x units of a religious medal costs c(x)=18x + 16. the revenue is r(x)=26x. both cost and revenue…

to produce x units of a religious medal costs c(x)=18x + 16. the revenue is r(x)=26x. both cost and revenue are in dollars. a. find the break - even quantity. b. find the profit from 550 units. c. find the number of units that must be produced for a profit of $80. a. units is the break - even quantity. (type an integer.) b. the profit for 550 units is $ c. units make a profit of $80. (type an integer.)

to produce x units of a religious medal costs c(x)=18x + 16. the revenue is r(x)=26x. both cost and revenue are in dollars. a. find the break - even quantity. b. find the profit from 550 units. c. find the number of units that must be produced for a profit of $80. a. units is the break - even quantity. (type an integer.) b. the profit for 550 units is $ c. units make a profit of $80. (type an integer.)

Answer

Explanation:

Step1: Set cost equal to revenue for break - even

Set $C(x)=R(x)$. So, $18x + 16=26x$.

Step2: Solve for $x$

Subtract $18x$ from both sides: $16 = 26x-18x$, which simplifies to $16 = 8x$. Then $x=\frac{16}{8}=2$.

Step3: Calculate profit function

The profit function $P(x)=R(x)-C(x)=26x-(18x + 16)=26x-18x - 16=8x-16$.

Step4: Find profit for 550 units

Substitute $x = 550$ into the profit function: $P(550)=8\times550-16=4400 - 16=4384$.

Step5: Find $x$ for a profit of $80$

Set $P(x)=80$, so $8x-16 = 80$. Add 16 to both sides: $8x=80 + 16=96$. Then $x=\frac{96}{8}=12$.

Answer:

a. 2 b. 4384 c. 12