Question

1. (30 points) A firm produces two goods, A and B, and their production uses the
same resource. The company has already purchased b tons of this resource that
cannot be returned. Hence, it must be all used up during production. The firm
needs to allocate the resource between the production of its products to maximize
its total revenue. The revenue generated by the two products (in millions of
pounds) are given by
Product A : 1200 − qA2 − (S4 + 1)
2
Product B : 1400 − (qB − (S5 + 1))2
where qA and qB denote the amount of the resource used in the production of
product A and B, respectively, and S4 and S5 are the fourth and fifth digits of
your candidate number, respectively.
(a) (15 points) Use the method of Lagrange multipliers to determine the optimal
allocation of the resource between the production of the two products that
maximize the firm’s total revenue.
(b) (15 points) Let b = 17 and assume that the firm is offered one additional ton
of the resource for the price of 0.2 million pounds. Should the firm purchase
the extra ton of the resource?

Answer 1

Answer:

Plastic containers are poor conductor of heat, so food stored in it will not hurt us when we hold it, whereas metal containers will transfer the heat.

Answer 2

Answer:

Refer the attachment:)