Profits is calculated as sales revenue minus costs. Costs are likely to change with sales. Greater the output, higher the costs.
If the demand is price inelastic, rise in price will lead to lower output sold but increased sales revenue. But when output sold is lower costs are lower. Therefore, profits will increase not just from higher sales revenue but also from lower costs
Therefore. a producer operating on inelastic portion of demand curve should increase price to increase profits
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