Question

The cost of producing pots is the initial investment, $175, plus $3.50 in materials per pot. Therefore, the function C(p) = 175 + 3.5p defines the cost, C, of producing a number of pots, p. To the nearest cent, how much will it cost to produce 125 pots? (Enter only the number without the dollar sign, such as 25.03 for twenty-five dollars and 3 cents.)
How many pots can be produced if the budget is limited to $450?

Answer 1

Q1. The answer is 612.50

The function is C(p) = 175 + 3.5p
p - the number of pots

If we need to produce 125 pots, then p = 125
C(p) is then C(125). So calculate C(125)
C(125) = 175 + 3.5 * 125 = 175 + 437.5 = 612.5
So, the production of 125 pots costs $612.5.


Q2. The answer is 78.

The function is C(p) = 175 + 3.5p
C(p) is the cost of producing a p number of pots.
If our budget is $450, then C(p) = 450. So, we need to calculate p.
C(p) = 450
C(p) = 175 + 3.5p
450 = 175 + 3.5p
3.5p = 450 - 175
3.5p = 275
p = 275/3.5
p = 78.57

So, the number of pots that can be produced for $450 is 78.
We got 78.57 for p, but it must be rounded to the smallest rounded number because you cannot produce 0.57 of a pot.