Carlo and Anita make mailboxes and toys in their craft shop near Lincoln Each mailbox requires 1 hour of work from Carlo and 3 hours from Anita. Each toy requires 1 hour of work from Carlo and 4 hours from Anita. Carlo cannot work more than 7 hours per week and Anita cannot work more than 24 hours per week. If each mailbox sells for $8 and each toy sells for $14, then how many of each should they make to maximize their revenue? What is their maximum revenue?

maximize the revenue they should make 6 toys

The maximum revenue is $84

Step-by-step explanation:

given data

Carlo mailbox = 1

Anita mailbox =  3

Carlo toy = 1

Anita   toy =  4

Carlo work = 7 hours per week

Anita work =  24 hours per week

mailbox sells = $8

toy sells = $14

solution

we consider here number of mailboxes is m

and  m ≥ 0    .................1

and

number of toys is t

and t ≥ 0         .................2

so we can say equation will be  

1m + 1t ≤ 7      ...................3

3m + 4t ≤ 24  ....................4

solve these equation 1,2,3 and 4 in graph and we will get graph that is attach here

we get here are 4 corner that is

The corner points are: (0, 0), (7, 0), (4, 3), (0, 6)

so objective revenue function is

F(m, t) = 8m + 14t      ..........................5

put here all value of corner

F(0, 0) = $0

F(7, 0) = 7×8 = $56

F(4 , 3) = 4×8 + 3×14 = $74

F(0 , 6) = 6×14  = $84

so here maximize the revenue they should make 6 toys

The maximum revenue is $84

i just took the test, the correct answer is .. 31.5 in.

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it