Question

A pottery maker makes seven varieties of plate, each of which it sells in sets of four. The making of varieties 1, 2, and 3 requires a complex and time-consuming process; thus, the pottery maker has decided that it would rather not make these varieties unless it can make and sell at least 15 sets of plates of varieties 1, 2, and 3 combined Suppose also that the demand for variety 6 is at most 5 sets, that the capacity available to the pottery maker means that the total number of plates made cannot exceed 50 sets, and that there are no other limitations on what the pottery maker can make and sell Formulate mathematically the problem of maximising total profit.

Answer 1

Mthematical model is following:

Let Xi = 1, if any set of variety i is made, otherwise Xi = 0

Yi = number of sets of variety i made

Max Y1+Y2+Y3+Y4+Y5+Y6+Y7   (assuming that each variety has same unit profit)

s.t.

50Xi - Yi >= 0

Y1+Y2+Y3+Y4+Y5+Y6+Y7 <= 50

Y1+Y2+Y3-15X1 >= 0

Y1+Y2+Y3-15X2 >= 0

Y1+Y2+Y3-15X3 >= 0

Y6 <= 5

Xi binary

Yi >= 0