Question

Mary Pell owns three different companies that create different genres of movies. Each company specializes in one kind of movie. The table below lists the 3 companies, the cost to make each movie and the selling price per movie. Company Cost per movie Selling Price per movie Marginal Profit per Movie Now- See-Me $150 $250 $100 Illusions $200 $275 $75 Movies-R-Us $75 $100 $25 Mary’s goal is simple…maximize her total profit by determining the number of movies to be made and sold while working within constraints. (36 pts, 6 each) a). Identify the unknowns.

b). Write the objective function.

c). Write the constraint that captures that at least 1200 movies, in total, must be made.

d). Mary cannot produce more than 800 movies, in total, from Now-You-See and Illusions companies combined. Write this constraint.

e). The number of Now-You movies sold must be less than the number of movies sold from Movies-R-Us. Write the constraint.

f). They cannot spend more than $20,000 to produce movies made by Illusions. Write this constrain

Answer 1

SOLUTION:-

(i) Let x be the no. of movies of Noice - See - Me

y be the no. of movies of illusion

z be the no. of movies of Movies - R - US

Cost Selling price Marginal project

Noice-See-Me(x) 150 250 100

Illusions (y) 200 275 75

Movies R-US (z) 75 100 25

(ii) Objective Junction = Z1

= Manimize = 100x + 75y + 25z

(iii) x + y + z   1200

(iv) x + y 800

(v) x < z

(vi) 150x + 200y + 75z   20,000

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