(25 points) An auto manufacturer produces two versions of its flagship sedan, on
ID: 1203512 • Letter: #
Question
(25 points) An auto manufacturer produces two versions of its flagship sedan, one with an automatic transmission (A) and one with a manual transmission (M). The manufacturer can make a profit of $40,000 for each A version sold and $20,000 for each M version sold. Each version is made with two types of labor, assembly labor and finishing labor. Automatic cars require 20 labor hours of assembly and 30 labor hours of finishing. The manual version requires 20 labor hours of assembly and 10 hours of finishing. The goal of the manufacturer is to maximize profit given the following three daily production constraints: 1. The manufacturer can produce a maximum of 100 automatic transmissions per day. 2. The manufacturer can employ a maximum of 6,000 labor hours for assembly per day. 3. The manufacturer can employ a maximum of 4,200 labor hours for finishing per day.
(e) Suppose the maximum amount of assembly labor is lifted from 6,000 to 6,400 hours per day. Calculate the new optimal values of M, A, and profit. How does profit change when the assembly labor constraint is relaxed by 400 hours? What is the shadow price of assembly labor hours? Explain this shadow price in words.
Explanation / Answer
Given the above constraints: (solved using excel solver)
total units 'A' = 60, 'M' = 240 & total profit = $7,200,000...optimal values
now with assembly labor lifted from 6000 to 6400, profit increases by $200,000
total units 'A' = 50, 'M' = 270 & total profit = $7,400,000...optimal values
Shadow cost also referred to as opportunity cost i.e where actual cost is not known
Here by increasing the ALH by 400, profit increased by $ 200,000, so the shadow cost of ALH per hour
=200,000/400 = $500 per hour
Qty Assembly labor hours (ALH) Finishing labor hours (FLH) Profit per unit Total ALH Total FLH Total profit A 60 20 30 40000 1200 1800 2400000 M 240 20 10 20000 4800 2400 4800000 Total 6000 4200 7200000Related Questions
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