Share Tool + Management Kdan Cloud Topic 4 Questions A= Tv Tv □ v OV Comment & Markup T Annotation Editor FAX OCR OCR Convert Fax Search Outlines Q Search Optimization Unconstrained optimization Constrained optimization (... factory 3, respectively. The company receives an order for 2000 units. How should the production of these 2000 units be allocated so as to minimize the total production cost? 75. Products A and B are substitutes. The relationship between the price PA (in € per unit) and the number QA of units that can be sold of product A and the price pB (in € per unit) and the number qB of units that can be sold of product B can be described by S9A = 10-2PA + PB 3PB 9B = 15+ 2PA The production cost of each product A and B amounts to €1 per unit. (a) Suppose that both products are produced by the same manufacturer. Find the prices PA and PB such that the profit of the manufacturer reaches a maximal value. (It suffices to find a relative maximum.) (b) Suppose that the products are produced by a different manufacturer, so manufacturer A pro- duces product A and manufacturer B produces product B. Suppose moreover that manufac- turers A and B are competitors and do not enter into an agreement about the prices PA and PB. i. Suppose that manufacturer B sells his product at a price pg 4. Find the value PA that (absolutely) maximizes the profit of manufacturer A. ii. Suppose that manufacturer B sells his product at a price pB. Find the value PA that (absolutely) maximizes the profit of manufacturer A. (PB will appear in the answer.) iii. Suppose that manufacturer A sells his product at a price PA. Find the value PB that (absolutely) maximizes the profit of manufacturer B. (PA will appear in the answer.) iv. Find the values PA and PB that arise when both manufacturers A and B try to maximize their profits independently from one another. 76. The production function of a company is given by q = 2qL1/2 +3qc1/2, where q denotes the output amount, qr, the input amount of labour and qc the input amount of capital. A unit of labor costs 2 monetary units and a unit of capital costs 1 monetary unit. The unit price for the output is 8 monetary units. Determine the maximal profit the company can make. 195% 2 17