K05

A. Calculate how many units of output can be produced with 4 units of labor and 400 units of capital and with 16 units of labor and 1,600 units of capital. Are returns to scale increasing, constant, or diminishing?

B. Calculate the change in the marginal product of labor as labor grows from 4 to 16 units, holding capital constant at 400 units. Similarly, calculate the change in the marginal product of capital as capital grows from 400 to 1,600 units, holding labor constant at 4 units. Are returns to each factor increasing, constant, or diminishing?

C. Assume now and throughout the remainder of the problem that labor and capital must be combined in the ratio 4L:400K. How much output could be produced if Cherry has a constraint of L = 4,000 and K = 480,000 during the coming production period?

D. What are the marginal products of each factor under the conditions described in part C?

P9.3 LP Setup and Interpretation. The Syflansyd Nut Company has enjoyed booming sales following the success of its "Sometimes You Feel Like a Nut, Sometimes You Don't" advertising campaign. Syflansyd packages and sells four types of nuts in four different types of mixed-nut packages. These products include bulk (B), economy (E), fancy (F), and regular (R) mixed-nut packages. Each of these packages contains a different mixture of almonds (A), cashews (C), filberts (F), and peanuts (P). Based on its contracts with current suppliers, the company has the following daily inventory of each of the following nuts: almonds, 8,000 ounces; cashews, 7,000 ounces; filberts, 7,500 ounces; and peanuts, 10,000 ounces.

Given available inventory, it is management's goal to maximize profits by offering the optimum mix of the four package types. Profit earned per package type is as follows:

Bulk

Economy

Fancy

Regular

The composition of each of the four package types can be summarized as follows:

Ounces per Package

Bulk

Economy

Fancy

Regular

Almonds

Cashews

Filberts

Peanuts

Total

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