(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 + x tt + xot  xot +xtt +xct   xii > 0    b) chow-chow relish   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.

Attached are two homework problems that I need help with and I am not understanding it so well. Any questions please let me know. unit_7_hw.docx

1. Find the pooled variance and estimated standard error of the mean for the studies below. Then calculate the t ratio for each study. Make sure to write down/type up the t ratio formula and steps in calculation:n1 S1 n2 S250  4  20   130  2  60   560  4  20   32. A social psychologist is studying mass communication randomly assigned 87 volunteers to one of two experimental groups. 63 participants were instructed to get their news from a month only from TV, and 24 were instructed to get their news for a month only from the internet. After one month, all participants were tested on their knowledge of several political issues. Given the mean ratings of political news were 26 for the TV group (S2TV=3) and 24.5 for the internet group (S2internet=7), Did the researcher find a significant difference between two experimental groups? Test at .05 significance level. Write down/type up all calculation steps, relevant formulas, and critical values.3. A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows.Ethnic Group A: n = 15 = 55 S2 = 6.5Ethnic Group B: n= 23 = 51 S2 = 4.5a) What is the pooled estimate of the population variance?b) What is the standard error of the mean?c) Are two ethnic groups are significantly different from each other on social role approval (α=0.05).Note: write down/type up all calculation steps, relevant formulas, and critical values