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Sagot :
Answer:
The least number of meals Amelia needs to cater in order to begin making profit = 38 meals.
Step-by-step explanation:
Given - Amelia runs a catering business. Based on her records, her weekly
profit can be modeled by P= -2x² + 152x - 150, where x is the
number of meals she caters and P is her profit. When P is negative,
Amelia losses money.
To find - What is the least number of meals Amelia needs to cater in order
to begin making profit.
Proof -
As given, P = -2x² + 152x - 150
Now,
Above the break-even point, she only get profit
The break -even point is a point where there is no profit, and no loss.
Now,
For break-even point,
[tex]\frac{dP}{dx} = 0[/tex]
⇒[tex]\frac{d}{dx}( -2x^{2} + 152x - 150) = 0[/tex]
⇒-4x + 152 = 0
⇒- 4x = - 152
⇒4x = 152
⇒x = [tex]\frac{152}{4}[/tex] = 38
∴ we get
If Amelia caters at least 38 meals , then she makes Profit.
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