Figure 10(a) shows the feasible set of the nutrition problem in Example 1 of Section 3.3 and the straight line of all combinations of rice and soybeans for which the cost is 42 cents.
(a) The objective function is 21x + 14y. Give the linear equation (in slope-intercept form) of the line of constant cost c.
(b) As c increases, does the line of constant cost move up or down?
(c) By inspection, find the vertex of the feasible set that gives the optimal solution.