Question

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?

Answer 1

maximize the revenue they should make 6 toys

The maximum revenue is $84

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