Question

Considering the sensitivity report for a furniture company's production of desks and chairs, and the opportunity to acquire an additional 50 units of wood for $3,000, should the company make the purchase to maximize profits?

a. Yes, the company should acquire the additional 50 units of wood. Based on the shadow price for wood, profits will increase more than $3,000 if 50 additional units of wood are available.

b. No, the company should not acquire the additional 50 units of wood. The shadow price of wood is 45, and therefore profits will not increase enough to cover the cost of the additional wood.

c. No, the company should not acquire the additional 50 units of wood since both reduced costs are equal to 0.

d. Yes, the company should acquire the additional 50 units of wood since the allowable decrease for chairs is equal to 450."

Answer 1

To decide whether to purchase additional units of wood, compare the shadow price to the cost per unit. If the cost exceeds the shadow price, do not buy; otherwise, proceed if it increases profit. In the long run, firms can expand capacity to meet increased demand.

Step-by-step explanation:

The student's question pertains to a decision about whether to purchase additional units of wood based on a sensitivity report from linear programming or optimization results, given the shadow price of wood. If the shadow price (or marginal value of one additional unit of the resource) of wood is higher than the cost per unit of acquiring more wood, it is financially favorable for the company to purchase the additional wood, assuming the shadow price is applicable within the relevant range. However, if the shadow price is lower than the additional cost per unit, or if acquiring the additional units does not lead to a proportional increase in profit, the company should not make the purchase.

For instance, if the shadow price is $45 per unit of wood, purchasing 50 additional units at $3,000 implies a cost of $60 per unit ($3,000 / 50 units), which is higher than the shadow price. Therefore, the profit gain from using the extra 50 units of wood would not cover the acquisition cost, and the company should not buy the extra wood if profit maximization is the goal.

In a long-run scenario where demand has increased, the firm might consider expanding capacity, such as acquiring more personal computers (PCs) to boost efficiency and meet the higher production requirements dictated by market demand. This strategy allows the company to adjust its production function and better align resources with the increased level of output, minimizing bottlenecks and optimizing throughput.