(56) The Douglas family raises cattle on their farm in Virginia. They also have a large garden in which they grow ingredients for making two types of relish-chow-chow and tomato. These they sell in 16-ounce jars at local stores and craft fairs in the fall. The profit for a jar of chow – chow is $2.25, and the profit for a jar of tomato relish is $1.95. The main ingredients in each relish are cabbage, tomatoes, and onions. A jar of chow-chow must contain at least 60% cabbage, 5% onions, and 10% tomatoes and a jar of tomato relish must contain at least 50% tomatoes, 5% onions, and 10% cabbage. Both relishes contain no more than 10% onions. The family has enough time to make no more than 700 jars of relish. In checking sales records for the past 5 years, they know that they will sell at least 30% more chow-chow than tomato relish. They will have 300 pounds of cabbage, 350 pounds of tomatoes, and 30 pounds of onions available. The Douglas family wants to know how many jars of relish to produce to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve by using the computer.
SOLUTION
a) x = amount (oz) of ingredient i in jar of j, where i = cabbage, tomato,onions and
j =chow-chow, tomato
Maximize Z ={ 2.25} (xcc + xtc+ xoc) + { 195 } (xct + xtt +xot)
16 16
Subject to
xcc + xtc +xoc + xct +xtt +xot <(700)(16)
xcc >.60
xcc + xtc + xoc
xtt > .50, xoc >.05
xct +xtt +xot xcc +xtc +xoc
xoc < .10, xtc >.10
xcc +xtc + xoc xcc + xtc + xoc
xot < .10, xot > .05
xct + xtt +xot xct + xtt +xot
xcc + xct < (300)(16)
xtc +xtt < (350)(16)
xoc + xot < (30)(16)
xcc + xtc + xoc > 1.3 xct > .10
xct + xtt + xot xot +xtt +xct
xii> 0
b) chow-chowrelish tomato relish
xcc = 4,608 oz xct = 192 oz
xtc = 2,688 oz xtt= 1,632 oz
xoc = 384 oz xot= 96 oz
7,680 oz 1,920 oz
480 jars 120 jars
Z = $1,313.66
Help me set this problem up in excel. Solve by putting data in excel QM to generate a sensitivity report and LP max. Explain the steps on how to insert data in QM to solve and get sensitivity report.
