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Linear Programming : Maximizing Profits

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A California grower has a 50 acre farm on which to plant strawberries and tomatoes. The grower has available 300 hours of labor per week and 800 tons of fertilizer, and has contracted for shipping space for a maximum of 26 acres' worth of strawberries and 37 acres' worth of tomatoes. An acre of strawberries requires 10 hours of labor and 8 tons of fertilizer, whereas an acre of tomatoes requires 3 hours of labor and 20 tons of fertilizer. The profit from an acre of strawberries is $400, and the profit from an acre of tomatoes is $300. The farmer wants to know the number of acres of strawberries and tomatoes to plant to maximize profits.

a. formulate a linear programming model for this problem
b. solve this model using graphical analysis

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The expert examines maximizing profits for linear programming.

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Linear Programming problem- Maximizing profits

A manufacturer of outdoor clothing makes wax jackets and trousers. Each jacket requires 1 hour to manufacture, whereas each pair of trousers takes 40 minutes. The material for a jacket cost £32 and those for a pair of trousers cost £40. The company can devote only 34 hours per week to the production of jackets and trousers, and the firm's total weekly cost for materials must not exceed £1200. The company sells the jackets at a profit of £12 each and the trousers at a profit of £14 per pair. Market research indicates that the firm can sell all of the jackets that are produced, but that it can sell at most half as many pairs of trousers as jackets.

How many jackets and trousers should the firm produce each week to maximize profit?

If the firm could obtain one more unit of production time, what would be the effect on the production mix? Hence, determine the value to the firm of that one extra unit of input.

Due to the changes in demand, the company has to change its profit margin on a pair of trousers. Assuming that the profit margin on a jacket remains at £12 and the manufacturing constraints are unchanged, find the minimum and maximum profit margins on a pair of trousers which the company can allow before it should change its strategy for optimum output.

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