Express the weekly profit earned using the variable cost per unit and the fixed cost.
TP=TR-TC
TP= P(9+33p-p^2)-10(9+33p-p^2)+100
Please help me solve this! I am BEGGING.
THANK YOU SO MUCH
To express the weekly profit using the given variables, we first need to understand the meaning of the variables in the equation:
- TP represents the total profit.
- TR represents the total revenue.
- TC represents the total cost.
- P represents the price per unit.
- p represents the number of units sold.
- The equation provided: TP = P(9 + 33p - p^2) - 10(9 + 33p - p^2) + 100 is used to calculate the total profit.
Now, let's solve the equation step-by-step to get the weekly profit:
1. Start with the equation: TP = P(9 + 33p - p^2) - 10(9 + 33p - p^2) + 100.
2. Multiply each term inside the parentheses by P and -10:
TP = 9P + 33Pp - P^2 - 90 - 330p + 10p^2 + 100.
Simplify the equation: TP = 10p^2 + 33Pp - P^2 - 330p + 9P + 10.
3. Rearrange the equation in descending order of p^2, p, and constants:
TP = 10p^2 + (33P - 330)p + (- P^2 + 9P + 10).
4. Now, consider fixed costs (FC) and variable costs (VC) to separate the equation:
TP = Total Revenue - Total Cost.
Total Revenue (TR) = Pp.
Total Cost (TC) = FC + VC = - P^2 + 9P + 10.
TP = Pp - (- P^2 + 9P + 10).
5. Simplify TP = Pp + P^2 - 9P - 10.
Therefore, the expression for the weekly profit (TP) in terms of variable cost per unit (P) and fixed cost is:
TP = Pp + P^2 - 9P - 10.