The price per pizza yields a demand of 2000 pizza is $6, when advertising is increased to $600
Step-by-step explanation:
Direct and inverse proportion:
The weekly demand for a company's frozen pizzas varies directly as the amount spent on advertising and inversely as the price per pizza
Assume that the weekly demand for a company's frozen pizzas is y, the amount spent on advertising is $x and the price per pizza is $z
∵ The weekly demand "y" varies directly as the amount spent on
advertising "$x"
∴ y ∝ x
∵ The weekly demand "y" varies inversely as the price per pizza "$z"
∴ y ∝ [tex]\frac{1}{z}[/tex]
∴ y ∝ [tex]\frac{x}{z}[/tex]
∴ [tex]y=k*\frac{x}{z}[/tex]
To find the value of k substitute x , y and z by their initial amount
∵ The price per pizza is $5
∴ z = 5
∵ $500 is spent each week on ads
∴ x = 500
∵ The demand is 2000 pizzas
∴ y = 2000
- Substitute these values in the equation of y above
∵ [tex]2000=k*\frac{500}{5}[/tex]
∴ 2000 = k(100)
- Divide both sides by 100
∴ 20 = k
- Substitute the value of k in the equation
∴ [tex]y=20*\frac{x}{z}[/tex]
∵ Advertising is increased to $600
∴ x = 600
∵ The demand is 2000 pizzas
∴ y = 2000
- To find the price per pizza "z" under this condition substitute the
values of x and y in the equation below
∵ [tex]y=20*\frac{x}{z}[/tex]
∴ 2000 = 20 × [tex]\frac{600}{z}[/tex]
- Divide both sides by 20
∴ 100 = [tex]\frac{600}{z}[/tex]
- Multiply both sides by z
∴ 100 z = 600
- Divide both sides by 100
∴ z = 6
∴ The price per pizza = $6
The price per pizza yields a demand of 2000 pizza is $6, when advertising is increased to $600
Learn more:
You can learn more about direct and inverse proportion in brainly.com/question/10708697
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