Answer to Question #259104 in Calculus for Anuj

Question

Micros Unlimited corporation (a local distributor of micro computers) sells one of its 586-based system on a volume

discount as follows: 1 to 5 units at a price of $4495 per unit, units 6 through 10 at a price of $ 4095 per unit, and

any unit in excess of 10 at a price of $3775 per unit.

i. Determine the cost function and draw its graph.

ii. What are the total and average cost s of 4 units ?

iii. What are the total and average cost s of 15 units?

iv. How many units were purchased if the total charge was $58,050 ?

v. How many units were purchased if the average charge was $4035?

Answer 1

i)

p - price, x - units

$p(x)=\begin{cases} 4495 & 1\le x\le 5 \\ 4095 & 6\le x \le 10\\ 3775&x>10 \end{cases}$

ii)

average cost:

$p(4)=\$4495$

total cost:

$4\cdot 4495=\$17980$

iii)

average cost:

$\frac{5\cdot4495+5\cdot4095+5\cdot3775}{15}=\$4121.67$

total cost:

$15\cdot4121.67=\$61825$

iv)

$58050=5\cdot4495+5\cdot4095+4\cdot3775$

were purchased:

$5+5+4=14$ units

v)

$4035=\frac{5\cdot4495+5\cdot4095+3775n}{N}$

$N=10+n$

Then:

$4035(10+n)=42950+3775n$

$260n=2600$

$n=10$

were purchased:

$N=5+5+10=20$ units