but do not solve the Kane Manufacturing has a division that produces two models

Question

but do not solve the Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y unts of model B. To model B grate requires 5 ib of cast iron and 3 min of labor. The profit for each model A grate is s production of grates per day, how many grates of each model should the division produce per day in order to maximize Kane's profts P produce each model A requires 3 tb of cast inon and 7 min of labor. To produce each 1.00, and the profit for each model B grace is $2.20. 1300 ib of canst iron and 1300 min of labor are available for the subject to the constraints not solve the loans, where x is homeowner loans in millions of dollars and y is auto loans in milions of deliars. On the average, homeowner Management has also stipulated that the total amount of homeowner loans should be greater chan or equal to 4 times loans have a 10% annual rate of return, whereas auto loans yield a 14% annual rate of the total amount of automobile loans. Determine the amount of loans of each type Madison shouid extend to each category in order to maximize its returns, p a relationship between loan amounts K20

Explanation / Answer

I am solving the first question Q3 as per Chegg guidelines, post multiple question to get the remaining problem answer i.e. Q4

Q3)

Let the number of units of model A be x

Let the number of units of model B be y

Since we want to maximize the profit, which will be given by

Maximize P = (number of models of A) * profit on model A + (number of models of B) * profit on model B

=> 1.00x + 2.20y

Hence first blank will be Maximize

Second blank will be P = 1.00x + 2.20y

Now we require 3lb of cast iron for product A and 5 lbs of cast iron for Product B, hence we get the constraints on cast iron as

3x + 5y <= 1300 [Third blank]

Now we require 7 mins of labor for product A and 3mins of labor for Product B, hence we get the constraints on labor as

7x + 3y <= 1300 [Fourth blank]

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