1. [-/12.5 Points] DETAILS HARMATHAP12 14.3.001. The cost (in dollars) of manufacturing one item is given by C(x, y) = 20 + 2x + By where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. (a) If the hourly cost of labor is $20, and the material costs $8 per pound, what is the cost of manufacturing one of these items? $ (b) Find the partial derivative of C with respect to x. CX = Interpret the partial derivative of C with respect to x. O The cost (in dollars) of manufacturing one item will increase by $8 for a $1 increase in y if x is held constant. O The cost (in dollars) of manufacturing one item will increase by $2 for a $1 increase in x if y is held constant. O The cost (in dollars) of manufacturing one item will increase by $20 for a $1 increase in x if y is held constant. O The cost (in dollars) of manufacturing one item will increase by $2 for a $1 increase in y if x is held constant. O The cost (in dollars) of manufacturing one item will increase by $8 for a $1 increase in x if y is held constant. Need Help? Read It Watch It 2. [-/12.5 Points] DETAILS HARMATHAP12 14.3.003.MI. The total cost of producing 1 unit of a product is C(x, y) = 38 + 6x + 2y + dollars where x is the cost per pound of raw materials and y is the cost per hour of labor. (a) If labor costs are held constant, find the function that describes the rate at which total cost increases for each increase of $1 per pound in material cost. (b) If material costs are held constant, find the function that describes the rate at which total cost increases for each $1 per hour increase in labor costs. Need Help? Read It Master It3. [-/12.5 Points] DETAILS HARMATHAP12 14.3.007. The joint cost (in dollars) for two products is given by C(x, y) = 25 + x7 + 3y + 2xy where x represents the quantity of product X produced and y represents the quantity of product Y produced. (a) Find the marginal cost with respect to x if 5 units of product X and 12 units of product Y are produced. $ Interpret your answer, If y remains at 12, the expected change in cost for a 6th unit of x is this amount. O If x remains at 5, the expected change in cost for a 13th unit of y is this amount. If y remains at 5, the expected change in cost for a 13th unit of x is this amount. O If x remains at 12, the expected change in cost for a 6th unit of y is this amount. (b) Find the marginal cost with respect to y if 5 units of product X and 12 units of product Y are produced. Interpret your answer O If x remains at 12, the expected change in cost for a 6th unit of y is this amount. O If y remains at 5, the expected change in cost for a 13th unit of x is this amount. O If y remains at 12, the expected change in cost for a 6th unit of x is this amount. O If x remains at 5, the expected change in cost for a 13th unit of y is this amount. Need Help? Read It 4. [-/12.5 Points] DETAILS HARMATHAP12 14.3.011. Suppose that the joint cost function for two products is C(x, y) = 1100 In(xy + 6) + 15,000 dollars. (a) Find the marginal cost with respect to x. (b) Find the marginal cost with respect to y. Need Help? Read It Watch It5. [W125 Points] DETAILS PREVIOUS ANSWERS HARMATHAP1214.3.U13.MI. Suppose that the production Function for a product is z = 9' 430', where x represents the number or work hours per month and y is the number at available machines. (a) Determine the marginal productivity oF x. '|.-' {'3} X X (b) Determine the marginal productivity of y. Need Help