1. The Whitt Window Company, a company with only three employees, makes two differentkindsofhand-craftedwindows:awood-framedandanaluminum-framedwindow.Thecompanyearns$300profitforeachwood-framedwindowand$150profitforeachaluminum-framed window. Doug makes the wood frames and can make 6 per day. Lindamakes the aluminum frames and can make 4 per day. Bob forms and cuts the glass and canmake 48 square feet of glass per day. Each wood-framed window uses 6 square feet of glassandeach aluminum-framed windowuses 8 squarefeetofglass.

Thecompanywishestodeterminehowmanywindowsofeachtypetoproduceperdaytomaximizetotal profit.Formulatethelinearprogrammingmodel forthis problem.

2. The Primo Insurance Company is introducing two new product lines: special risk insuranceand mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit onmortgages.

Managementwishestoestablishsalesquotasforthenewproductlinestomaximizetotalexpectedprofit. Thework requirements areasfollows:

3.Weenies and Buns is a food processing plant which manufactures hot dogs and hot dogbuns. They grind their own flour for the hot dog buns at a maximum rate of 200 pounds perweek. Each hot dog bun requires 0.1 pound of flour. They currently have a contract withPigland, Inc., which specifies that a delivery of 800 pounds of pork product is delivered everyMonday. Each hot dog requires 1/4 pound of pork product.All the other ingredients in the hotdogs and hot dog buns are in plentiful supply. Finally, the labor force at Weenies and Bunsconsists of 5 employees working full time (40 hours per week each). Each hot dog requires 3minutes of labor, and each hot dog bun requires 2 minutes of labor. Each hot dog yields aprofitof$0.88, and eachbunyields aprofit of$0.33.

Weenies and Buns would like to know how many hot dogs and how many hot dog buns theyshouldproduceeach week so as to achievethehighest possibleprofit.

Formulatealinearprogrammingmodelforthisproblem.