2. A rancher faces the profit function =1100, -30-20, +1400, - 200, where Qu = side of beef and Q, = hides. Since there are two sides of beef for every hide, it foilows that output must be in the proportion Qi=202. (a) At what level of output will the rancher maximise profit? (b) Confirm that at the critical outputs the profit is maximised

(b) Towns A and B are 12 km apart. A cyclist leaves A and travels to B at an average speed of y km/h. From B, he returns immediately to A with an average speed reduced by 2 km/h. (i) Find, in terms of y, the time taken for the journey from A to B. (ii) Find, in terms of y, the time taken for the return journey. (iii) Given that the total time spent to travel from A toB and back to A is 5 hours, write an equation satisfied by y. (iv) Solve the equation written in part (iii). (v) Give a simple reason why one of the values of y obtained in part (iv) is not valid.

The marginal cost and marginal revenue of a company are MC (q) = 0.03q² − 1.5q + 35 and MR(q) 25, where q is the number of items manufactured. To increase profits, should the company increase or decrease production from each of the following levels? (a) 25 items: The company should production. (b) 50 items: The company should (c) 80 items: The company should production. production. =

3.) The revenue equation (in billions of dollars) for corn production in the United States is approximated by R(x)=0.016x² +1.034x+11.338 Where x is in billions of bushels. For example if you have 10 billion bushels, then x = 10. (Data from www.usda.gov) a.) Find the marginal revenue function b.) Find and interpret the marginal revenue for 15 billion bushels c.) Find and interpret the marginal revenue for 20 billion bushels

A farm that grows apples determined that their daily cost during peak season was C(a)=3.75a+350 a is a bushel of apples.  what are the farm's marginal cost and the farm's fixed costs ?