Download x y x = 75− 40 p+ 25q N(x,y) =10 x y

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Handout - Chapter 8
Math 167
Section 8.1
Ex 3. A company manufactures two models of bicycles. The weekly demand and
cost equations are
𝑝 = 230 − 9𝑥 + 𝑦
𝑞 = 130 + 𝑥 − 4𝑦
𝐶(𝑥, 𝑦) = 200 + 80𝑥 + 30𝑦
where $p is the price of Bicycle A, $q is the price of Bicycle B, x is the weekly
demand of Bicycle A, y is the weekly demand of Bicycle B, and C(x, y) is the
cost function. Find the weekly revenue function R(x, y) and the weekly profit
function P(x, y). Evaluate R(10, 15) and P(10, 15).
Section 8.2
Ex 4. A company spends $x per week on newspaper advertising and $y per week
on television advertising. Its weekly sales were given by 𝑆(𝑥, 𝑦) = 10𝑥 0.4 𝑦 0.8 .
Find 𝑆𝑥 (3000,2000) and 𝑆𝑦 (3000,2000), and interpret the results.
Section 8.3
Ex 4. A store sells two brands of film. The store pays $2 for each roll of Brand A
film and $3 for each roll of Brand B film. A consulting firm has estimated the
daily demand equations for these two products, respectively, to be:
𝑥 = 75 − 40𝑝 + 25𝑞
𝑦 = 80 + 20𝑝 − 30𝑞
where p is the selling price for Brand A and q is the selling price for Brand B.
How should the store price each brand of film in order to maximize daily
profits?
Section 8.5
Ex 3. A manufacturing company has a production model given by
𝑁(𝑥, 𝑦) = 10𝑥 0.6 𝑦 0.4 , where x is the number of units of labor and y is the
number of units of capital required to produce N(x, y) units of the product.
Each unit of labor costs $30 and each unit of capital costs $60. If $300,000 is
budgeted for production, determine how that amount should be allocated to
maximize the production.