A grower estimates that if he picks his apple crop now, he will obtain 1000 boxes of apples, which he can sell at $3 per box. However, he thinks his crop will increase by 120 boxes of apples for each week he delays picking, but that the price will drop at a rate of 15c per box per week; in addition, he estimates that approximately 20 boxes per week will spoil for each week he delays picking.
(a) When should he pick his crop to obtain the largest total cash return? How much will he receive for his crop at that time?
(b) Build a spreadsheet (see Appendix A) to calculate the profit for 0, 1, 2, ..., 6 weeks.