An open pit mine produces ore from three different working faces. The ore from face 1 has an average grade of 7.2g/t and the corresponding average grades at faces 2 and 3 are 1.8g/t and 4.3g/t respectively. Based on the production plan minimum production of 5000t/shift, 6000t/shift and 4000t/shift are required for faces 1, 2 and 3 respectively.

Ore from the three faces can be hauled to plants 1 and 2 for processing. Due to plant recovery considerations plant 1 can process ore that is blended to a grade ranging from 3.5g/t to 5g/t. Under the same considerations plant 2 can treat ore that is blended to a grade ranging from 1.5g/t to 4g/t. The crushers at plants 1 and 2 have capacities of 30000t/shift and 25000t/shift respectively (since there is no room for storage all ore from the plant comes straight and only to the crushers).

Determine the best mining plan from faces to plants if objective of management is to maximise ore production in tonnes per shift.

Management has set the following goals in order of priority:

1. Maximum utilisation of plant productive capacities per shift. Since the maximum capacities of plant 1 and 2 are not equal they should be differentiated in proportion to their maximum capacities.

2. Ensure that ore production from face 1, a high grade area, is as close as possible to the maximum of 18000t/shift.

Formulate this as a goal programming model.