Review 26 Course : K0644 - Business Mathematics Year : 2010
<ul><li>A firm produces three products A,B, and C that require processing by three machines I, II, and III. The time in hours required for processing one unit of each product by the three machines is given by the following table : </li></ul><ul><li>Machine I is available for 490 hours, machine II for 310 hours, and machine III for 560 hours. Find how many units of each product should e produced to make use of all the available time on the machines. </li></ul>Matrix Algebra Bina Nusantara A B C I 3 1 2 II 1 2 1 III 2 4 1
Differentiation <ul><li>If Total Revenue function, TR= q(20-0.1q) . Find the marginal revenue function. </li></ul><ul><li>2. If average cost, AC=0.03q + 1.2 + (3/q). Find marginal cost when q=100. </li></ul>Bina Nusantara University
Additional Differentiation Topics Determine the point elasticity of the demand equation : a. q = √500-P, when P = 400. b. P = 500 / (q 2 ), when q = 52 Bina Nusantara University
Curve Sketching <ul><li>Sketch the graph : </li></ul><ul><li>a. Y = x 2 -3x-10 </li></ul><ul><li>b. Y = 3x – x 3 </li></ul><ul><li>2. For the manufacturer’s product, the revenue function is given by r = 240q + 57q 2 – q 3 . Determine the output for maximum revenue. </li></ul>Bina Nusantara University
Multivariable Calculus <ul><li>Suppose a monopolist is practicing price discrimination is the sale of a product by charging different prices in two separate markets. In market A the demand function is Pa=100-qa and Pb=84-qb </li></ul><ul><li>Where qa and qb are the quantities sold per week in A and B, and Pa and Pb are the respective prices per unit. If the monopolist’s cost function is C=600+4(qa+qb). How much should be sold in each market to maximize profit? What selling prices give this maximum profit? Find the maximum profit. </li></ul>Bina Nusantara University
2. The production function for a firm is f( l,k )=12 l +20 k - l 2 -2 k 2 The cost to the firm of l and k is 4 and 8 per unit, respectively. If the firm wants the total cost of input to be 88, find the greatest output possible, subject to this budget constraint. Bina Nusantara University
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