It is assumed that Florida grapefruit products are sold in six markets: domestic fresh

white seedless grapefruit, export fresh white seedless grapefruit, domestic fresh red seedless

grapefruit, export fresh red seedless grapefruit, domestic grapefruit juice, and export grapefruit

juice. Let k index these markets. The inverse demand equation for market k is given by

(7) P, = a, b,Q,

where Pk is the price in market k, Q, is the quantity sold in market k, and ak and bk are the

parameters of the demand equation.

 Let X, be the boxes of variety v allocated to processing. Let processing costs be denoted

by PC and are assumed to be invariant across the two varieties. Juice yield for both varieties

is estimated to be 4.8 SSE gallons per box.

 Given these assumptions, a quadratic programming model which gives the competitive

allocation of fresh fruit between the domestic and export markets and between fresh and

processed utilization is

 6 2
(8a) max (aQk 1/2bkQ) PC-X,
 k-C v-1


(8b) s.t. Q + Q2 + Xi Z <- 0

(8c) Q +Q4 + X-Z2 < 0

(8d) -4.8X, 4.8X2 + Qs + Q, < 0

(8e) Q,,...,Q, XI,2 0

 The objective function given by (8a) maximizes the sum of the areas under the demand

functions for each of the six markets adjusted for the cost of producing grapefruit juice. The