I got the break-even point right, but I need help for the last two questions in 2)a): The weight of cheese which should be sold to maximise profit is, and the sale of cheese which will result in the lowest profit. And the unit is kg, rounded to the nearest g, not sure about this either.

A farm produces cheese and sells it by weight. The corresponding revenue function a is R(x)=95x and the daily cost function b is C(x)=43+141x0.86. where R(x) and C(x) are in euros and x denotes the weight of cheese sold, in kilograms. For practical reasons (milk supply, storage and display space), the maximum amount of cheese that the farm can produce and sell daily is 28.5 kilograms. 1) State an interval of length at most 10 grams that contains a break-even c point for the sales of cheese, where the break-even point is expressed in kilograms. Explain how you know this interval contains a break-even point. 2) Prove that the sale of cheese will produce a maximum profit. Hence, find how many kilograms of cheese should be sold to maximise profit d. In addition, in order to avoid the worst possible financial situation, the farmers would also like to know selling how many kilograms of cheese will result in the greatest loss. In order to answer this question, find how many kilograms of cheese sold will minimise profit d. 2) a) The theorem we will be using for question 2) is the max-min theorem the intermediate value theorem the mean value theorem The weight of cheese which should be sold to maximise profit is kilograms, rounded to the nearest gram. The sale of cheese which will result in the lowest profit is kilograms, rounded to the nearest gram. Hints for writing your solution: i. State the assumptions of the max-min theorem, and verify that they hold true on the interval [0,28.5]. ii. Find dxdP, where P is the profit. iii. Remember that we want to find the values of x that correspond respectively to the maximum of and minimum of P. A farm produces cheese and sells it by weight. The corresponding revenue function a is R(x)=95x and the daily cost function b is C(x)=43+141x0.86. where R(x) and C(x) are in euros and x denotes the weight of cheese sold, in kilograms. For practical reasons (milk supply, storage and display space), the maximum amount of cheese that the farm can produce and sell daily is 28.5 kilograms. 1) State an interval of length at most 10 grams that contains a break-even c point for the sales of cheese, where the break-even point is expressed in kilograms. Explain how you know this interval contains a break-even point. 2) Prove that the sale of cheese will produce a maximum profit. Hence, find how many kilograms of cheese should be sold to maximise profit d. In addition, in order to avoid the worst possible financial situation, the farmers would also like to know selling how many kilograms of cheese will result in the greatest loss. In order to answer this question, find how many kilograms of cheese sold will minimise profit d. 2) a) The theorem we will be using for question 2) is the max-min theorem the intermediate value theorem the mean value theorem The weight of cheese which should be sold to maximise profit is kilograms, rounded to the nearest gram. The sale of cheese which will result in the lowest profit is kilograms, rounded to the nearest gram. Hints for writing your solution: i. State the assumptions of the max-min theorem, and verify that they hold true on the interval [0,28.5]. ii. Find dxdP, where P is the profit. iii. Remember that we want to find the values of x that correspond respectively to the maximum of and minimum of P