A tomato grower needs to ship early when prices are high and spoilage is low. She now has 25 tons on hand and by can add two tons a week by waiting. The current profit is $250 per ton but it will reduce $15 per ton for each week she delays. When should she ship to receive the maximum profit?

Question

Jax Riggs

Mathematics

22 November, 18:18

A tomato grower needs to ship early when prices are high and spoilage is low. She now has 25 tons on hand and by can add two tons a week by waiting. The current profit is $250 per ton but it will reduce $15 per ton for each week she delays. When should she ship to receive the maximum profit?

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Answers (1)

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Camren Burgess · Answer 1

On first week

Quantity of tomato = 25 tons

profit per ton = $250

So if she sells tomato on first week then total profit = 25 * 250 = $6250

On second week

Quantity of tomato = 27 ton

profit per kg = $ 235

So if she sells tomato on second week then total profit = 27 * 235 = $6345

On third week

Quantity of tomato = 29 ton

Profit per kg = $220

So if she sells tomato on third week then total profit = 29*220 = $6380

Now consider fourth week

Quantity of tomato = 31 ton

Price per kg = $205

So if she sells tomato on fourth week then total profit = 31*205 = $6355

so she must ship her tomatoes on third week i. e she will attain $ 6380 as profit.