A company manufactures x units of Product A and y units of Product B, on two machines, I and II. The company will realize a profit of $4/unit of Product A and a profit of $4/unit of Product B. Manufacturing 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. Manufacturing 1 unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of time available on Machine I and 3 hr of time available on Machine II in each work shift. (a) How many units of each product should be produced in each shift to maximize the company's profit? The maximum is P = at (x, y) = . (b) Suppose P = cx + 4y. Find the range of values that the contribution to the profit of 1 unit of Product A, the coefficient c of x, can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values (in hours) that the resource associated with the time constraint on Machine I can assume. ≤ (resource) ≤
A company manufactures x units of Product A and y units of Product B, on two machines, I and II. The company will realize a profit of $4/unit of Product A and a profit of $4/unit of Product B. Manufacturing 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. Manufacturing 1 unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of time available on Machine I and 3 hr of time available on Machine II in each work shift. (a) How many units of each product should be produced in each shift to maximize the company's profit? The maximum is P = at (x, y) = . (b) Suppose P = cx + 4y. Find the range of values that the contribution to the profit of 1 unit of Product A, the coefficient c of x, can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values (in hours) that the resource associated with the time constraint on Machine I can assume. ≤ (resource) ≤
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.CR: Chapter Review
Problem 70E: A company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three...
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A company manufactures x units of Product A and y units of Product B, on two machines, I and II. The company will realize a profit of $4/unit of Product A and a profit of $4/unit of Product B. Manufacturing 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. Manufacturing 1 unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of time available on Machine I and 3 hr of time available on Machine II in each work shift.
(a) How many units of each product should be produced in each shift to maximize the company's profit?
(c) Find the range of values (in hours) that the resource associated with the time constraint on Machine I can assume.
(d) Find the shadow price for the resource associated with the time constraint on Machine I.
The maximum is P = at
(b) Suppose P = cx + 4y. Find the range of values that the contribution to the profit of 1 unit of Product A, the coefficient c of x, can assume without changing the optimal solution.(x, y) =
.
≤ c ≤
(c) Find the range of values (in hours) that the resource associated with the time constraint on Machine I can assume.
≤ (resource) ≤
(d) Find the shadow price for the resource associated with the time constraint on Machine I.
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