You are starting a small business to sell toys. The demand for toys are unlimit and far exceeds your production capacity
Posted: Thu Apr 28, 2022 2:57 pm
You are starting a small business to sell toys. The demand for
toys are unlimit and far exceeds your production capacity. The
selling price for one toy is $10 and you are price takers in the
toy market (i.e. your production will not affect the market price).
The annual production depends solely on labor working hours:
ππππ’ππ πππππ’ππ‘πππ = 6 Γ π
Where N denotes the annual labor working hours. Moreover, in the
labor market, the laborβs working hours depend directly on hourly
wage you pay:
π = β2500 + 1000 Γ π€
Where w denotes the hourly wage. In the first year of your
business, you have a budget of $25000 as labor cost. Your goal is
to maximize your annual profit = revenue β labor cost.
a. (6 points)How do you formulate the annual revenue function from
selling toys in terms of hourly wage w ?
b. (6 points)How do you formulate the total labor cost function in
terms of w?
c. (8 points)Write down a non-linear program for this optimization
problem.
toys are unlimit and far exceeds your production capacity. The
selling price for one toy is $10 and you are price takers in the
toy market (i.e. your production will not affect the market price).
The annual production depends solely on labor working hours:
ππππ’ππ πππππ’ππ‘πππ = 6 Γ π
Where N denotes the annual labor working hours. Moreover, in the
labor market, the laborβs working hours depend directly on hourly
wage you pay:
π = β2500 + 1000 Γ π€
Where w denotes the hourly wage. In the first year of your
business, you have a budget of $25000 as labor cost. Your goal is
to maximize your annual profit = revenue β labor cost.
a. (6 points)How do you formulate the annual revenue function from
selling toys in terms of hourly wage w ?
b. (6 points)How do you formulate the total labor cost function in
terms of w?
c. (8 points)Write down a non-linear program for this optimization
problem.