Chapter 4.2, Problem 26E

Set up and solve Exercises 23–29 by the simplex method.

Income A baker has 150 units of flour, 90 of sugar, and 150 of raisins. A loaf of raisin bread requires 1 unit of flour, 1 of sugar, and 2 of raisins, while a raisin coke needs 5, 2, and 1 units, respectively.

(a) If raisin bread sells for $1.75 a loaf and raisin cake for $4.00 each, how many of each should be baked so that gross income is maximized?

(b) What is the maximum gross income?

(c) Does it require all of the available units of flour, sugar, and raisins to produce the number of loaves of raisin bread and raisin cakes that produce the maximum profit? If nut, how much of each ingredient is left over? Compare any leftover lo the value of the relevant slack variable.