Question

Select all of the constraints that apply to this situation $1.25x when x <12$12.00 + $0.75(x-12) when X_>12$1.25x when x _>120.75x when x >12$12.00 + $0.75x when x >12

Answer 1

We want to write expressions that describe the cost of the cookies. Let say we sell x cookies. If x is less than 12, then the cost per cookie is 1.25. So the cost of x cookies would be the product of this numbers, so it would be

`1.25x,x<12`

Note that when x=12 the cost should be 12. Also note that for each extra cookie, starting at 12, each cookie costs 0.75. If we buy x cookies , to calculate the extra cookies, with respect to 12, we simply substract 12 from x and we multiply it by 0.75. This would be

`0.75\cdot(x\text{ -12)}`

as this is an additional cost to the 12, we add 12 to this expression. THen we get

`12+0.75\cdot(x\text{ -12)}`

Note that for this expression, when x=12, we get that the expression becomes

`12+0.75\cdot(12\text{ -12)=12}`

THis means that the expression applies from 12 and on, so we have the followin inequality12

`12+0.75\cdot(x\text{ -12), x}\ge12`