Question

A car rental agency has a budget of $1.56 million to purchase at most 100 new cars. The agency will purchase either subcompact cars at $12,000 each or mid-sized cars at $24,000 each. From past rental patterns, the agency decides to purchase at most 50 mid-sized cars and expects an annual profit of $8,000 per subcompact car and $13,000 per mid-sized car. How many of each type of car should be purchased to obtain the maximum profit while satisfying budgetary and other planning constraints? Find the maximum profit. Use the simplex method or Excel. Assume that all variables are nonnegative. Maximize f = -x + 2y + 4z subject to the following constraints: x + y + z â‰¤ 45 -x + y + z â‰¥ 10 x + y - z â‰¥ 5 x = y = z = f = This problem involves maximization with mixed constraints. A sausage company makes two different kinds of hot dogs, regular and all beef. Each pound of all-beef hot dogs requires 0.75 lb of beef and 0.2 lb of spices, and each pound of regular hot dogs requires 0.18 lb of beef, 0.3 lb of pork, and 0.2 lb of spices. Suppliers can deliver at most 1020 lb of beef, at most 600 lb of pork, and at least 500 lb of spices. If the profit is $1.50 on each pound of all-beef hot dogs and $1.00 on each pound of regular hot dogs, how many pounds of each should be produced to obtain maximum profit? (Round your answers to the nearest whole number.) all-beef hot dogs: lb regular hot dogs: lb What is the maximum profit? (Round your answer to the nearest whole number.) $ Nolan Industries manufactures water filters/purifiers that attach to a kitchen faucet. Each purifier consists of a housing unit that attaches to the faucet and a 60-day filter (sold separately) that is inserted into the housing. Past records indicate that on average, the number of filters produced per week should be at least 200. It takes 20 minutes to make and assemble each filter and 40 minutes for each housing. The manufacturing facility has at least 8,000 minutes per week for making and assembling these units, but due to certain parts supply constraints, the number of housing units per week can be at most 500. If manufacturing costs (for material and labor) are $6.80 for each filter and $8.50 for each housing unit, how many of each should be produced to minimize weekly costs? filters: housing units: Find the minimum cost. $

A car rental agency has a budget of $1.56 million to purchase at most 100 new cars. The agency will purchase either subcompact cars at $12,000 each or mid-sized cars at $24,000 each. From past rental patterns, the agency decides to purchase at most 50 mid-sized cars and expects an annual profit of $8,000 per subcompact car and $13,000 per mid-sized car. How many of each type of car should be purchased to obtain the maximum profit while satisfying budgetary and other planning constraints?

Find the maximum profit. Use the simplex method or Excel. Assume that all variables are nonnegative.

Maximize f = -x + 2y + 4z subject to the following constraints:
x + y + z â‰¤ 45
-x + y + z â‰¥ 10
x + y - z â‰¥ 5
x = y = z = f =

This problem involves maximization with mixed constraints.

A sausage company makes two different kinds of hot dogs, regular and all beef. Each pound of all-beef hot dogs requires 0.75 lb of beef and 0.2 lb of spices, and each pound of regular hot dogs requires 0.18 lb of beef, 0.3 lb of pork, and 0.2 lb of spices. Suppliers can deliver at most 1020 lb of beef, at most 600 lb of pork, and at least 500 lb of spices. If the profit is $1.50 on each pound of all-beef hot dogs and $1.00 on each pound of regular hot dogs, how many pounds of each should be produced to obtain maximum profit? (Round your answers to the nearest whole number.)

all-beef hot dogs: lb
regular hot dogs: lb

What is the maximum profit? (Round your answer to the nearest whole number.)
$

Nolan Industries manufactures water filters/purifiers that attach to a kitchen faucet. Each purifier consists of a housing unit that attaches to the faucet and a 60-day filter (sold separately) that is inserted into the housing. Past records indicate that on average, the number of filters produced per week should be at least 200. It takes 20 minutes to make and assemble each filter and 40 minutes for each housing. The manufacturing facility has at least 8,000 minutes per week for making and assembling these units, but due to certain parts supply constraints, the number of housing units per week can be at most 500. If manufacturing costs (for material and labor) are $6.80 for each filter and $8.50 for each housing unit, how many of each should be produced to minimize weekly costs?

filters:
housing units:

Find the minimum cost.
$

Added by Grant H.

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