A farmer wants to find the best time to take her hogs to market. The current price is 84¢ per pound, and her hogs weigh an average of 48 lbs. The hogs gain 3 lbs per week, and the market price for hogs is falling each week by 3¢ per pound. At what weight will the farmer break even, assuming the market price continues to fall at the same rate?

The farmer can determine the weight at which she would break even analysis by setting up and solving a simple equation based on the lowering market price and the increasing weight of the hogs.

Explanation:

To find the weight at which the farmer would break even given the conditions of the question, we must take into consideration two key factors in this scenario: the decreasing price per pound and the increasing weight of the hogs. We are told that the hog's weight increases by 3 lbs per week, and the price per pound drops by 3 ¢ per week. In the initial week, a hog therefore sells for $0.84 per pound and weighs 48lbs.

We can describe both of these changes using simple equations: P = 0.84-0.03w and W = 48+3w where P represents the price per pound after w weeks and W represents the weight of the hog after w weeks. The farmer breaks even when the total price of selling her hog remains constant, i.e., when P * W is constant. To find at what weight the hog should be sold to break even, we set P * W = 0.84 * 48 and solve.

This will give us the number of weeks the farmer should let the hogs grow, and by substituting this w into the weight equation, we can get the weight that will allow the farmer to break even. After you get the number of weeks, please don't forget to multiply it by 3 (the amount of pounds the hogs gain each week) and add the original weight of the hogs (48 lbs) to get the break-even weight.

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