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Homework Math # 6
Due Nov. 2
Texas A & M University
Fall 2011
1. [50 points] Use Matlab to solve the following nonlinear problem. Include
a graph of the feasible region and the contours of the nonlinear objective
function.Perth Mining Company operates two mines for the purpose of extracting gold and silver. For x days of operation, the Saddle Mine costs
$10, 000x2 1000x + 2000 and it yields 50 oz of gold and 3000 oz of silver.
For y days of operation, the Horseshoe Mine costs $12, 000y 2 500y + 3000
and it yields 75 oz of gold and 1000 oz of silver each of y day. Company management has set a target of at least 650 oz of gold and 18,000 oz of silver.
How many days should each mine be operated so that the target can be met
at a minimum cost?
2. A company interested in marketing a new carpet cleaner wants to examine the inuence of ve factors on consumer preferencepackage design, brand
name, price, a Good Housekeeping seal, and a money-back guarantee. There
are three factor levels for package design, each one diering in the location
of the applicator brush; three brand names (K2R, Glory, and Bissell); three
price levels; and two levels (either no or yes) for each of the two last factors.
The following table displays the variables used in the carpet-cleaner study,
with their variable labels and values.
Variable name
package
brand
price
seal
money
Variable label
package design
brand name
price
Good Housekeeping seal
money-back guarantee
Value label
A , B , C
K2R, Glory, Bissell
$1.19, $1.39, $1.59
no, yes
no, yes
Data
1,2,3
1,2,3
1,2,3
0,1
0,1
Source: IBM corporation, Example of Carpet Cleaner
The hypothetical data le Carpet.xls contains the results of the costumer
survey. The columns are in the order of above table with the specied data
values. Import the data to Matlab and let A,B,C,D,E be the columns 1
through 5 respectively.
1
How many costumers
a ) [2 points] were surveyed?
b ) [6 points] are interested in each package design A , B and C ?
c ) [10 points] are willing to pay the highest price for the package design
A , brand Glory, with seal and money-back guarantee?
d ) [10 points] would pay the lowest price for the package design B ,
brand Bissell, with no seal and no money-back guarantee?
e ) [7 points] are interested in seal and money-back guarantee?
f ) [5 points] are not interested in seal but want to have money-back
guaranteed?
2