Set up linear programming model in excel, solve using excel QM, assignment help

(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.