Question

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A grocer sells 30 loaves of bread a day. The cost is $2.50 per loaf. The grocer estimates that for each $0.50 increase in cost, 2 fewer loaves of bread will be sold per day. Let x represent the number of $0.50 increases in the cost of a loaf of bread.
For what number of $0.50 increases in the cost of a loaf of bread will the grocer's generated revenue be greater than zero?

Answer 1

30-(increase/0.5)*2=sold
i*s=revenue
i*30-(i^2/0.5)*2=r
I=7.5=>r=0
i=7=>r=14
7/0.5=15 number of increases in the cost

Answer 2

15 is the answer.

Explanation:

Initial number of selling = 30 at the cost $2.50 each

on increasing $0.50 cost on each we have 2 fewer selling

that is number of selling be x so its 30-2x

cost of selling for 30-2x will be = 2.50+0.50x

revenue = (30-2x)(2.5+0.5)

the value of x for which revenue is increased

(30-2x)(2.5+0.5x)>0

`(30-2x)(2.50+0.50x)\geq 0\\75+15x-5x-x^2\geq 0\\75+10x-x^2\geq 0\\x^2-10x-75\leq 0\\(x+5)(x-15)\leq 0\\-5\leq x\leq 15\\`

so the maximum value of x is 15