LP The Douglas Family, statistics homework help

LP The Douglas Family, statistics homework help

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.

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 + x tt + xot xot +xtt +xct

  xii > 0   

b) chow-chow relish   tomato relish

x_cc = 4,608 oz     x_ct = 192 oz

x_tc = 2,688 oz   x_tt = 1,632 oz

xoc = 384 oz  x_ot =   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.  NOTE: (Need sensitivity report sent with LPmax for information to use later.)

a. Formulate a linear programming model for this problem.

b. Solve by using the computer.

Create and set up excel spreadsheet

Solve using excel QM solver

Get LP max and sensitivity report

Complete and show correct answers  results in excel

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