Question

A craftsman builds two kinds of birdhouses, one for wrens and one for bluebirds. Each wren birdhouse takes 3 hours of labor and 4 units of lumber. Each bluebird house requires 2 hours of labor and 10 units of lumber. The craftsman has available 80 hours of labor and 100 units of lumber, and he wants to build at least 6 wren houses. Wren houses profit $8 each and bluebird houses profit $16 each. How many of each kind of birdhouses should be built in order to maximize total profit?  Formulate this as a linear programming problem (i.e., DO NOT solve it.)

Answer 1

Answer: Maximize the objective value, because its the profit

No. of wren houses to make is 25 units

No. of bluebird houses to make is 0 units

Maximum profit is $200

Explanation:

W is no. of wren houses

B is no. of bluebird houses

Labor hours: 3*W + 2*B  ≤ 80---- Eqn1
lumber units: 4*W + 10*B  ≤ 100---- Eqn2

W >= 6---- Eqn3

Profit of Objective, maximize 8*W + 6*B = z

Cell no.	B	C	D	E	F	G	H
6		W	B		Total		Max capacity
7	Decision variable
8	Maximize	8	6	0	0.00
9	Subject to
10	equation 1	3	2	0	0.00	<=	80
11	equation 2	4	10	0	0.00	<=	100
12	equation 3	1	0	0	0.00	>=	6

formulae

Cell no.	B	C	D	E	F	G	H
6		W	B		Total		Max capacity
7	Decision variable
8	Maximize	8	6	0	=C8*$C$7 + D8*$D$7
9	Subject to
10	equation 1	3	2	0	=C10*$C$7 + D10*$D$7	<=	80
11	equation 2	4	10	0	=C11*$C$7 + D11*$D$7	<=	100
12	equation 3	1	0	0	=C12*$C$7 + D12*$D$7	>=	6

solver

Solution

Cell no.	B	C	D	E	F	G	H
6		W	B		Total		Max capacity
7	Decision variable	25.00	0.00
8	Maximize	8	6	0	200.00
9	Subject to
10	equation 1	3	2	0	75.00	<=	80
11	equation 2	4	10	0	100.00	<=	100
12	equation 3	1	0	0	25.00	>=	6

W= 25

B= 0

Optimum= $200