9.6 graph quadratic using properties (homework)\nscore: 9/20 answered: 9/20\nquestion 14\na store manager…

9.6 graph quadratic using properties (homework)\nscore: 9/20 answered: 9/20\nquestion 14\na store manager determines that the revenue from shoes, when the price for a pair of shoes is t dollars,\nwill be ( h(t)=-t^{2}+36 t ) dollars.\nwhat price should be charged to maximize revenue? dollars\nwhat will the revenue be at this price? dollars

9.6 graph quadratic using properties (homework)\nscore: 9/20 answered: 9/20\nquestion 14\na store manager determines that the revenue from shoes, when the price for a pair of shoes is t dollars,\nwill be ( h(t)=-t^{2}+36 t ) dollars.\nwhat price should be charged to maximize revenue? dollars\nwhat will the revenue be at this price? dollars

Answer

Explanation:

Step1: Find the price ( t ) that maximizes revenue

For a quadratic function ( y = ax^{2}+bx + c ), the vertex (which gives the maximum or minimum value) has its ( x )-coordinate at ( t=-\frac{b}{2a} ). In the function ( h(t)=-t^{2}+36t ), ( a=- 1) and ( b = 36 ). Using the formula ( t=-\frac{b}{2a} ), we substitute the values: ( t=-\frac{36}{2\times(-1)}=\frac{-36}{-2}=18 )

Step2: Find the maximum revenue

Substitute ( t = 18 ) into the function ( h(t)=-t^{2}+36t ). ( h(18)=-(18)^{2}+36\times18 ) First, calculate ( (18)^{2}=324 ) and ( 36\times18 = 648 ) ( h(18)=-324 + 648=324 )

Answer:

The price to maximize revenue is ( 18 ) dollars. The revenue at this price is ( 324 ) dollars.