The following description will be used in questions 3a to 3d and bonus III.   Consider a firm that produces output y using capital k and labor l, according to the technology described by f(k,l) ≥ y and following a restriction g(k,l) ≥M; where f and g are functions of k and l, and M is a nonnegative value. Let r be the rental rate for capital and w the wage rate.   If the firm takes its output y as given and chooses inputs k and l to minimize costs, then the firm’s cost minimization problem is:   minimize   rk +wl     ,  by choosing k,l subject to:  f(k,l) = y   and   g(k,l) ≥M       

Why is it important to study production functions such as f1 and f2?

The following description will be used in questions 1c and 1d. Figure 3 showcases the cost function as a function of the price of x1 for a production function fI. Once again, you are asked to complete the missing information, which is represented by capital letters I, J, and K.

Problem 4 Description: Two different Types of injection-molding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discolored. Two random samples, each of size 100, are selected, and 12 defective parts are found in the sample from machine 1 while 5 defective parts are found in the sample from machine 2. Is it reasonable to conclude at 0.04 level of significance that machine 1 produces higher higher fraction of defective parts than machine 2?   Use Excel to do all the computations. Answer all the questions below and upload your Excel file to the last question and submit.

The American Stroke Association estimates that there are approximately 795,000 people who suffer a stroke each year in the United States, and of these, nearly 129,000 lead to death.  Calculate the percentage of people in the US that died last year as a result of suffering a stroke.

In 2012 the population of Malaysia is 28.3 million while the population of the US is 314.4 million. Calculate how many times larger the population of the US is compared to Malaysia.

The Belen family is completing their tax return, and they are filling out the itemized deductions form. For medical expenses, they have expenses of $3824 for the year; the form requires them to reduce this amount by 6.75% of their total income to find the deductible medical expenses.  If their total income is $48,385, which one of the following calculations will give the deductible medical expenses?

In addition to paying federal income taxes, many states require individuals to also pay state income tax.  Single people living in the state of Minnesota who earn between $25,100 and $82,400 fall into the 7% tax bracket.  This means they pay $1,340 plus 7% of their income over $25,100 in taxes.  Jordan Barnett is a Minnesota resident who earns $63,780.  Calculate the amount of money that Jordan would pay in Minnesota income taxes.  Be sure to write down the mathematical expression used in your calculation on your paper! Input your answer only in dollars and cents.

In July of 2022, it was estimated that the National Debt of the United States was 30.5 trillion dollars and the population of the United States was 332,900,000.  If the National Debt was evenly distributed amongst the entire population, calculate the debt per person.  Round your answer to the nearest dollar.

True or False: the spinal cord is part of the central nervous system.