Question about Marginal Rate of Technical Substitution

Problem 7.1 Marginal Rate of Technical Substitution. The following production table provides estimates of the maximum amounts of output possible with different combinations of two input factors, X and Y. (Assume that these are just illustrative points on a spectrum of continuous input combinations.)
A. Do the two inputs exhibit the characteristics of constant, increasing, or decreasing marginal rates of technical substitution? How do you know?
B. Assuming that output sells for $3 per unit, complete the following tables:
X Fixed at 2 Units
Y Fixed at 3 Units
C. Assume that the quantity of X is fixed at 2 units. If output sells for $3 and the cost of Y is $120 per day, how many units of Y will be employed?
D. Assume that the company is currently producing 162 units of output per day using 1 unit of X and 3 units of Y. The daily cost per unit of X is $120 and that of Y is also $120. Would you recommend a change in the present input combination? Why or why not?
What is the nature of the returns to scale for this production system if the optimal input combination requires that X = Y?
Question 7.1 Is use of the least-cost input combinations (technical efficiency) a necessary condition for profit maximization? Is it a sufficient condition? Explain.

Question 7.5 Explain why the MP/P relation is deficient as the sole mechanism for determining the optimal level of resource employment.

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The solutions provides answers to questions that deal with marginal rate of technical substitution, marginal product, Marginal Revenue Product, returns to scale, optimal level of resource employment