Answer :
To determine the vendor's monthly profit when selling 600 pretzels, let's break down the problem step by step.
1. Calculate the Total Cost (C(x)) for 600 pretzels:
The cost function is given by:
[tex]\[ C(x) = 0.63x + 800 \][/tex]
Substituting [tex]\(x = 600\)[/tex]:
[tex]\[ C(600) = 0.63(600) + 800 = 378 + 800 = 1178 \][/tex]
So, the total cost for 600 pretzels is [tex]$1178. 2. Calculate the Total Revenue (R(x)) for 600 pretzels: The revenue function is given by: \[ R(x) = 2.75x \] Substituting \(x = 600\): \[ R(600) = 2.75(600) = 1650 \] So, the total revenue from selling 600 pretzels is $[/tex]1650.
3. Calculate the Profit (P(x)) for 600 pretzels:
Profit is given by the difference between revenue and cost:
[tex]\[ P(x) = R(x) - C(x) \][/tex]
Substituting the values for revenue [tex]\(R(600) = 1650\)[/tex] and cost [tex]\(C(600) = 1178\)[/tex]:
[tex]\[ P(600) = 1650 - 1178 = 472 \][/tex]
Therefore, when the vendor sells 600 pretzels in a month, he makes a profit of $472.
1. Calculate the Total Cost (C(x)) for 600 pretzels:
The cost function is given by:
[tex]\[ C(x) = 0.63x + 800 \][/tex]
Substituting [tex]\(x = 600\)[/tex]:
[tex]\[ C(600) = 0.63(600) + 800 = 378 + 800 = 1178 \][/tex]
So, the total cost for 600 pretzels is [tex]$1178. 2. Calculate the Total Revenue (R(x)) for 600 pretzels: The revenue function is given by: \[ R(x) = 2.75x \] Substituting \(x = 600\): \[ R(600) = 2.75(600) = 1650 \] So, the total revenue from selling 600 pretzels is $[/tex]1650.
3. Calculate the Profit (P(x)) for 600 pretzels:
Profit is given by the difference between revenue and cost:
[tex]\[ P(x) = R(x) - C(x) \][/tex]
Substituting the values for revenue [tex]\(R(600) = 1650\)[/tex] and cost [tex]\(C(600) = 1178\)[/tex]:
[tex]\[ P(600) = 1650 - 1178 = 472 \][/tex]
Therefore, when the vendor sells 600 pretzels in a month, he makes a profit of $472.