Amanufacturer produces two types of bottled coffee drinks: cappuccinos and cafés au lait. each bottle of cappuccino requires 6 ounces of coffee and 2 ounces of milk and earns a profit of $0.40. each bottle of café au lait requires 4 ounces of coffee and 4 ounces of milk and earns a profit of $0.50. the manufacturer has 720 ounces of coffee and 400 ounces of milk available for production each day. to meet demand, the manufacturer must produce at least 80 coffee drinks each day. let x = the number of cappuccino bottles and y = the number of café au lait bottles. identify the constraints on the system other than x ≥ 0 and y ≥ 0. x + y 80 0.4x + 0.5y 100 6x + 4y 720 2x + 4y 400 6x + 2y 720 4x + 4y 400 complete the objective function. p = x + y

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

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answer: your answer is a