sza2016

19.10.2021 • 

Mathematics

Formulate and solve the following linear program:A firm wants to determine how many units of each of two products (products A and E) they should produce to make the most money. The profit in the manufacture of a unit of product A is $100 and the profit in the manufacture of a unit of product E is $87. Although the firm can readily sell any amount of either product, it is limited by its total labor hours and total machine hours available. The total labour hours per week are 4,000. Product A takes 5 hours of labour per unit and product E takes 7 hours of labour per unit. The total machine hours are 5,000 per week. Product A takes 9 hours of machine time per unit and product E takes 3 hours of machine time per unit.Write the Objective Function and Constraints for this problem.Solve for the best mix of product A and E using Microsoft Excel solver, andReport the maximum value of the Objective function.Please provide screen shots or scanned images of your Microsoft Excel Solver Reports.

Ответ:

smartie80

23.10.2022

Mathematics

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ninth year

Step-by-step explanation:

Given the general form of an exponential equation;

P = a(1 +r)^t

We can now write in this particular case;

y = 4 * 10^6(1 + 0.07)^t

The year in which y reaches 7 * 10^6 dollars is

7 * 10^6 =  4 * 10^6 (1 + 0.07)^t

7 * 10^6/4 * 10^6 = (1 + 0.07)^t

1.75 = (1 + 0.07)^t

ln(1.75)= ln(1 + 0.07)^t

ln(1.75) = t ln(1 + 0.07)

0.5596 = 0.06766t

t = 0.5596/0.06766

t = 8 years

So, in the ninth year;

y =  4 * 10^6 (1 + 0.07)^t

y = 4 * 10^6 (1 + 0.07)^9

y = 7.35 * 10^6

Hence, the player's earnings first exceed $7,000,000 in the ninth year.

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