I need help with part D below, i thought the function would be y=x/3 + y/2.
1. You produce sandwiches for the Perk cof�ee stand. Sandwiches require 3 tablespoons of mayonnaise
(x) and 2 tablespoons of mustard (y)
(a) Write the production function for sandwiches and plot the isoquant curves that correspond to
production of 1, 5 and 10 sandwiches.
(b) Because UCSC has virtually no other options on Science Hill, you somehow actually have orders
for 50 sandwiches. How many of each ingredients do you need to use to minimize your costs?
Assume mustard costs 10 cents per tablespoon and mayonnaise costs 20 cents each. What is your
resulting total cost of producing these 50 sandwiches?
(c) Draw an isocost curve consistent with the prices of inputs and level of production just given.
Carefully label the slope.
(d) A technological revolution happens; companies have �gured out how to sell premixed mayonnaise
and mustard. There are two brands Mayostard and Mustardayonnaise. The two products
are basically identical though Mayostard (x) is priced at 50 cents per sandwich while Mustarday-
onnaise (y) is priced at 40 cents per sandwich. Redo each of the three previous steps assuming
you use Mayostard and Mustardayonnaise to produce your sandwiches.
To solve part D, we need to adjust our production function and calculate the new cost of producing the sandwiches using the prices of Mayostard and Mustardayonnaise.
The new production function will be:
y = x/3 + y/2
Now let's calculate the cost of producing 50 sandwiches using the prices of Mayostard and Mustardayonnaise.
Let's assume Mayostard (x) is priced at 50 cents per sandwich, and Mustardayonnaise (y) is priced at 40 cents per sandwich.
To minimize costs while producing 50 sandwiches, we need to find the optimal combination of x and y that minimizes the cost function.
We can set up the cost function as follows:
Cost = (Price of Mayostard * x) + (Price of Mustardayonnaise * y)
Cost = (0.50 * x) + (0.40 * y)
Now, substituting the production function into the cost function, we get:
Cost = (0.50 * (3y - 4)) + (0.40 * y)
Simplifying the equation:
Cost = (1.50y - 2) + 0.40y
Cost = 1.90y - 2
Next, we set the cost to be 0 and solve for y:
0 = 1.90y - 2
2 = 1.90y
y = 2/1.9
y ≈ 1.05
Now, substitute this value of y back into the production function to find the value of x:
x = 3y - 4
x ≈ 3(1.05) - 4
x ≈ 3.15 - 4
x ≈ -0.85
However, since we can't have a negative quantity of sandwiches, we can set x = 0 and y = 1.05.
Therefore, to minimize costs and produce 50 sandwiches using Mayostard and Mustardayonnaise, you would need 0 tablespoons of Mayostard and approximately 1.05 tablespoons of Mustardayonnaise.
To calculate the total cost, substitute these values into the cost function:
Total Cost = (0.50 * x) + (0.40 * y)
Total Cost = (0.50 * 0) + (0.40 * 1.05)
Total Cost = 0 + 0.42
Total Cost = 0.42 dollars
So, the resulting total cost of producing 50 sandwiches using Mayostard and Mustardayonnaise would be approximately 42 cents.
Now, for part (c), we need to draw an isocost curve consistent with the prices of inputs and level of production. To do this, we can choose different combinations of x and y (in the feasible range) and plot the points on a graph. Connect these points to obtain the isocost curve. The slope of the isocost curve represents the rate of exchange between Mayostard (x) and Mustardayonnaise (y).
Finally, part (d) asks you to redo the previous steps using the new prices for Mayostard and Mustardayonnaise. Adjust the cost function and solve for the optimal combination of x and y, and then calculate the total cost of producing 50 sandwiches using the new prices.
I hope this helps you solve part D of your question! Let me know if you have any further doubts or need additional assistance.