1) The joint cost (in thousands of euros) for two products X and Y can be given by the following formula: C(x, y) = 40 + y^2 + 3x + 2xy + (x^2) y + y^3 where x represents the quantity of product X that is produced and y represents the quantity of product Y produced. • If 12 units of product X and 20 units of product Y are produced, what are the marginal costs? • What product line should be expanded in the current level of production?
1) The joint cost (in thousands of euros) for two products X and Y can be given by the following formula: C(x, y) = 40 + y^2 + 3x + 2xy + (x^2) y + y^3
where x represents the quantity of product X that is produced and y represents the quantity of product Y produced.
• If 12 units of product X and 20 units of product Y are produced, what are the marginal costs?
• What product line should be expanded in the current level of production?
2) A firm can produce up to 500 units each week. If its average cost function is C(x) = 500/x + 1500 and its total revenue function is given by: R(x) = 1600x − x^2
• What production maximizes profit? What is the maximum profit for that production level?
• What production makes the profit equal to zero? (that point is called the break-even point)
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