Use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand and others using technology. \(x+y=4\) \(x-y=2\)

Nutrition One serving of Campbell Soup Company's Campbell's Pork \& Beans contains 5 grams of protein and 21 grams of carbohydrates. A typical slice of "lite" rye bread contains 4 grams of protein and 12 grams of carbohydrates. a. I am planning a meal of beans on toast and wish to have it supply one-third of the U.S. RDA for protein (see Exercise 43 ) and 80 grams of carbohydrates. How should I prepare my meal? (Fractions of servings are permitted.) b. Is it possible to have my meal supply the same amount of protein as in part (a) but only 60 grams of carbohydrates? Protein Supplements Exercises \(45-48\) are based on the following data on three popular protein supplements. (Figures shown correspond to a single serving. \begin{tabular}{|r|c|c|c|c|} \hline & Protein \((\mathrm{g})\) & Carbohydrates \((\mathrm{g})\) & Sodium \((\mathrm{mg})\) & Cost \((\$)\) \\ \hline Designer Whey (Next) & 18 & 2 & 80 & 0.50 \\ \hline Muscle Milk (Cytosport) & 32 & 16 & 240 & 1.60 \\ \hline Pure Whey Protein Stack (Champion) & 24 & 3 & 100 & 0.60 \\ \hline \end{tabular}

Supply and Demand (from the GRE Economics Test) In the market for soybeans the demand and supply functions are \(Q_{D}=100-10 P\) and \(Q_{S}=20+5 P,\) where \(Q_{D}\) is quantity demanded, \(Q_{S}\) is quantity supplied, and \(P\) is price in dollars. If the government sets a price floor of \(\$ 7,\) what will be the resulting surplus or shortage?

Equilibrium Price In June 2001 the retail price of a 25-kilogram bag of cornmeal was \(\$ 8\) in Zambia; by December the price had risen to \(\$ 11 .\) The result was that one retailer reported a drop in sales from 15 bags per day to 3 bags per day. \({ }^{10}\) Assume that the retailer is prepared to sell 3 bags per day at \(\$ 8\) and 15 bags per day at \(\$ 11 .\) Find linear demand and supply equations, and then compute the retailer's equilibrium price.

Th Exercises \(21-30\), use technology to obtain approximate solutions graphically. All solutions should be accurate to one decimal place. (Zoom in for improved accuracy.) $$ \begin{aligned} 2 x+8 y &=10 \\ x+y &=5 \end{aligned} $$

V Management (from the GMAT) A manager has \$6,000 budgeted for raises for four full-time and two part-time employees. Each of the full-time employees receives the same raise, which is twice the raise that each of the part-time employees receives. What is the amount of the raise that each full-time employee receives?