6.) a deli sells 640 sandwiches per day at a price of $8.00 each. a market survey shows that for every $0.10 reduction in price, 40 more sandwiches will be sold. how much should the deli charges for a sandwiches in order to maximize revenue?

The demand function is

... q(p) = 640 + 40(8.00-p)/0.10 . . . a drop in price of 0.10 sells 40 more sandwiches

... q(p) = 3840 -400p . . . . . . . . . expanded form

... q(p) = 400(9.60 - p) . . . . . . . . factored form

The revenue is the product of price and the quantity sold.

... R(p) = p·q(p)

... R(p) = 400p(9.60 - p)

This is the equation of a quadratic function with zeros at p=0 and p=9.60. Since the zeros of a parabola are symmetric about its vertex, the vertex (maximum) will be halfway between those values, at p=4.80.

The deli should charge $4.80 for a sandwich to maximize revenue.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

i need points

step-by-step explanation:

sorry bubs