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?

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.