Can someone help me with this math question(A-level maths)

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KatheO11
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#1
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#1
This is question. I will kindly appreciate your help. It’s a modelling question.

A company made a particular type of children’s toy.
The annual profit made by the company is modelled by the equation

: P = 100- 6.25 (x-9)^2

Where P is the profit measured in thousands of pounds and x is the selling price of the toy in pounds.

A sketch of of P against X is in figure 1 (the sketch a downwards parabola, as if it were a negative quadratic, but is not in this case)

a) Using the model, explain why £15 is not a sensible selling price for the toy

B) given that the company made an annual profit of more than £80,000,

Find according to the model, the least possible selling price for the toy.

The company wishes to maximise its annual profit, state according to the model,

C) (i) the maximum possible annual profit
(ii) The selling price of the toy that maximises the annual profit.
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vc94
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#2
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#2
Which part do you need help with?
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Banshee123
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#3
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#3
(Original post by KatheO11)
This is question. I will kindly appreciate your help. It’s a modelling question.

A company made a particular type of children’s toy.
The annual profit made by the company is modelled by the equation

: P = 100- 6.25 (x-9)^2

Where P is the profit measured in thousands of pounds and x is the selling price of the toy in pounds.

A sketch of of P against X is in figure 1 (the sketch a downwards parabola, as if it were a negative quadratic, but is not in this case)

a) Using the model, explain why £15 is not a sensible selling price for the toy

B) given that the company made an annual profit of more than £80,000,

Find according to the model, the least possible selling price for the toy.

The company wishes to maximise its annual profit, state according to the model,

C) (i) the maximum possible annual profit
(ii) The selling price of the toy that maximises the annual profit.
OMG this cam up in the maths as exam. Just asking cuz idm, r u gonna sit this exam paper soon as your mock
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KatheO11
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#4
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#4
(Original post by Banshee123)
OMG this cam up in the maths as exam. Just asking cuz idm, r u gonna sit this exam paper soon as your mock
My teacher gave it to my class as homework. It’s practice towards our end of year exams.
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KatheO11
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#5
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#5
(Original post by vc94)
Which part do you need help with?
B and C, please.
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SerBronn
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#6
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#6
You write "a downwards parabola, as if it were a negative quadratic, but is not in this case".

That's a puzzling statement because it has the term (x-9)^2 so it's a quadratic and the coefficient of the quadratic term is negative.

Why doesn't it make sense to sell for 15? Because P would be negative so the company would lose money. Set P = 80 and solve the quadratic for the second part. Obviously the price which maximizes profit is 9.
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vc94
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#7
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(Original post by KatheO11)
B and C, please.
b) So P=80, try solving it...
c) The solution is staring at you in the graph!
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KatheO11
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#8
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Thanks guys!
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super9
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#9
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#9
Sure its not a downward parabola?
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SesMemKek
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#10
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#10
(Original post by KatheO11)
My teacher gave it to my class as homework. It’s practice towards our end of year exams.
Hey, if it would be alright do you still have this paper and the stats one to go with it that you could end to me thanks.
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QasimCh
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#11
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#11
C) Still don't understand?
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someone.1890
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#12
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#12
the turning point of the curve is (9,100) therefore the max possible profit is £100,000and selling price =£9.00
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