Answer to Question #258740 in Linear Algebra for Rakib

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.

$f(n) = \begin{cases} 4495\ n & \text{if } n\leq 5 \\ 2000 + 4095\ n &\text{if }5 < n \leq 10 \\ 5200 + 3775\ n & \text{if }10 < n \end{cases}$

ii.

Total cost = $4495*4 = $17,980, average cost is $17,980.4 = $4495

iii.

Total cost is $5200 + $3775*15 = $61, 825, average cost is $61, 825 / 15 = $4,121.67

iv.

If 10 units were purchased, the total cost was $42,950. As $58,050 is treated than $42,950, therefore there were purchased more than 10 units. So we have an equation 58,050 = 5200 + 2775*n. Or 2775*n = 52850. From here n = 14, so, there were purchased 14 units.

v.

Equation 2000 + 4095*n = 4035*n transforms to 2000 = -60*n, and it has no positive solution, so the number of purchased units is greater than 10

Equation 5200 + 3775*n = 4035*n transforms to 5200 = 260*n, and it has one solution, namely n = 20, so there were purchased 20 units.