Question

NO LINKS!!

The cost C (in dollars) of supplying recycling bins p% of the population in a rural township is given by C = 25000p/(100 - p). 0 ≤ p < 100.

a. Use a graphing utility to graph the cost function.

b. Find the costs of supplying bins to 25%, 50%, and 85% of the population. (Round your answers to the nearest dollar.)

cost to supply 25% C = $___________
cost to supply 50% C = $___________
cost to supply 85% C = $___________

c. According to this mode, would it be possible to supply bins to 100% of the residents? Choose yes or no
a. Yes
b. No

Explain. Choose one.
a. It is possible to supply bins to 100% of the residents, but it would be very costly.
b. This model is not an accurate representation of the cost to supply bins to 100% of the residents.
c. According to this model, would it be possible to supply bins to 100% of the residents?
a. Yes
b. No

Explain. Choose one
a. It is possible to supply bins to 100% of the residents, but it would be very costly.
b. This model is not an accurate representation of the cost to supply bins to 100% of the residents.
c. The model can work, but it is not accurate with populations over 25,000.
d. The function is undefined at p = 100
e. The function is a reasonable, defined value at p = 100.

Answer 1

(a) See attachment 1.

(b) Cost to supply 25% C = $8,333

Cost to supply 50% C = $25,000

Cost to supply 85% C = $141,667

(c) b. No

d. The function is undefined at p = 100

Explanation:

Given function:

`C=(25000p)/(100-p) \quad \quad 0 \leq p < 100`

where:

• C is the cost (in dollars)
• p is the percentage of the population

Part (a)

See attachment 1 for the graph of the function.

Part (b)

To find the costs of supplying bins to 25%, 50%, and 85% of the population, find the y-values of the points on the graph when p = 25, p = 50 and p = 85. (See attachment 2).

• Cost to supply 25% C = $8,333
• Cost to supply 50% C = $25,000
• Cost to supply 85% C = $141,667

Part (c)

According to this model, it would NOT be possible to supply bins to 100% of the residents.

As the function is a rational function, the function is undefined when p = 100, as when p = 100 the denominator is zero.

Answer 2

• 25% : $333
• 50% : $500
• 85% : $1667
• 100% : not possible (undefined)

Explanation:

You want various values provided by the cost function C = 25000/(100-p).

Graph

The attachment shows a graph.

Costs

The costs of supplying bins to various fractions of the population are ...

• 25% : $333
• 50% : $500
• 85% : $1667

Supply 100%

According to the model, it is not possible to supply 100% of the population.

d. The model is undefined at p = 100.