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The simplex algorithm is to continue in this manner, alwaysperforming basis exchanges which improve the objective function,until no more exchanges are possible. We conclude with an example:Buzz Buzz Buzz Coffee has on hand 1 kg of coffee grounds, 1 gallonof milk and 10 cups of sugar. They can use these to make espressos,containing 8 grams of grounds and no milk or sugar; lattes,containing 15 grams of grounds, 0.0625 gallons of milk and 0.125cups of sugar; or caf´e cubano, containing 7.5 grams of grounds, nomilk and 0.125 cups of sugar. They will be able to sell all theyproduce, which they will sell at prices of $2 for espressos, $4 forlattes and $5 for a caf´e cubano.

Question 10. (5 points) Let e, l and c be the number ofespressos, lattes and caf´es cubanos manufactured, and let g, m ands be the amounts of grounds, milk and sugar left over when they aredone. Let p be the amount of money they take in. Record the linearequations relating e, l, c, g, m, s and p.

Question 11. (15 points) Start at the point where no drinks aremade (so e = l = c = 0). Exchange one of these variables, in orderto increase p. Repeat the process of exchanging a basis variable toincrease p until there are no exchanges which will make p larger.How many of each drink should be made?