28. Chase Quinn wants to expand his cut-flower business. He has 12 additional acres on which he intends to plant lilies and gladioli. He can plant at most 7 acres of gladiolus bulbs and no more than 11 acres of lilies. In addition, the number of acres planted to gladioli G can be no more than twice the number of acres planted to lilies L. The inequality L + 2G 10 represents his labor restrictions. If his profits are represented by the function f(L, G) = 300L + 200G, how many acres of lilies should he plant to maximize his profit?

Question

28.   Chase Quinn wants to expand his cut-flower business. He has 12 additional acres on which he intends to plant lilies and gladioli. He can plant at most 7 acres of gladiolus bulbs and no more than 11 acres of lilies. In addition, the number of acres planted to gladioli G can be no more than twice the number of acres planted to lilies L. The inequality L + 2G > 10 represents his labor restrictions. If his profits are represented by the function f(L, G)  = 300L + 200G, how many acres of lilies should he plant to maximize his profit?

bobpursley · Answer

make a graph of L vs G

Plot the line l+2G>10, then the line G=7, and L<11

Your area of allowed solutions will be enclosed by these lines, and the optima will be on one of the corner intersections. Test each corner with the profit function given.