Question

Carlo and Anita make mailboxes and toys in their craft shop near Lincoln. Each mailbox requires 4 hours of work from

Carlo and 4 hours from Anita. Each toy requires 2 hours of work from Carlo and 4 hours from Anita. Carlo cannot work
more than 20 hours per week and Anita cannot work more than 28 hours per week. If each mailbox sells for $15 and
each toy sells for $24, then how many of each should they make to maximize their revenue? What is their maximum
revenue?

Answer 1

Given that:!

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

and

number of toys is t

and t≥0

so we can say equation will be

1m + 1t ≤7

3m+ 4t≤ 2

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 =

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