A company makes outdoor cat houses and dog houses. Both houses use the same base
ID: 468358 • Letter: A
Question
A company makes outdoor cat houses and dog houses. Both houses use the same base, but each house has a different perimeter and roof. The company can either manufacture or purchase the pieces, and the cost is given in the table below. Also given is the manufacture time, in minutes.
The demand projected is 2800 for the cat houses and 2200 for the dog houses. The company has 220 hours (13200 minutes) of manufacture time available. (There is no overtime available).
Find the number of each piece that should be manufactured or purchased that meets demand but minimizes cost.
Component Manufacturing Time (minutes)
Base 1.1
Cat Perimeter 2.8
Dog Perimeter 2.6
Cat Roof 1.0
Dog Roof 1.7
(a)Write the linear program, in standard form, that is needed to solve the problem.
(b)Put the linear program from (a) into Excel to find the optimal solution.
(c)Which, if any, of the pieces were both purchased and manufactured?
Component Manufacture Purchase Base $5 $6 Cat Perimeter $38 $40 Dog Perimeter $34 $40 Cat Roof $7 $8 Dog Roof $8 $9Explanation / Answer
Let the number of manuafcured and purchased items be as below:
Base = x1, y1
Cat Perimeter = x2, y2
Dog Perimeter = x3, y3
Cat Roof = x4, y4
Dog Roof = x5, y5
The objective is to minimize the cost.
Thus, Minimize Z = 5x1 + 38x2 + 34x3 + 7x4 + 8x5 + 6y1 + 40y2 + 40y3 + 8y4 + 9y5
Subject to:
x1 + y1 >= 5000
x2 + y2 >= 2200
x3 + y3 >= 2800
x4 + y4 >= 2200
x5 + y5 >= 2800
1.1x1 + 2.8 x2 + 2.6x3 + 1x4 + 1.7 x5 <= 13200
The same data can be entered into Excel Solver for solving.
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