Solve the Problem A Determine the Number of Grill a Units and the Gas

question 7

Multiple Choice

Solve the problem.
-A manufacturer produces two models of a gas grill.Grill A requires 0.9 hr for assembly and 0.5 hr for packaging. Grill B requires 1.2 hr for assembly and 0.8 hr for packaging. The production Information and profit for each grill are given in the table. The manufacturer has 1,152 hr of labor Available for assembly and 716 hr of labor available for packaging. $\begin{array} { l | c | c | c } & \text { Assembly } & \text { Packaging } & \text { Profit } \\\hline \text { Grill A } & 0.9 \mathrm { hr } & 0.5 \mathrm { hr } & 80 \\\text { Grill B } & 1.2 \mathrm { hr } & 0.8 \mathrm { hr } & 110\end{array}$
a. Determine the number of grill A units and the number of grill B units that should be produced to Maximize profit assuming that all grills will be sold.
b. What is the maximum profit under these constraints?
c. If the profit on grill A units is 120 and the profit on grill B units is unchanged, how many of each Type of grill unit should the manufacturer produce to maximize profit?

• A) a. \(\mathrm { A } = 0 , \mathrm {~B} = 895\)
• b. Profit \(= 98,450\)
• c. 520 units of \(A\) and 570 units of B
• B) a. \(A = 520 , B = 570\)
• b. Profit = 57,656
• c. 1,280 units of A and 0 units of B
• C) a. \(\mathrm { A } = 520 , \mathrm {~B} = 570\)
• b. Profit \(= 104,300\)
• c. 1,280 units of \(\mathrm { A }\) and 0 units of \(\mathrm { B }\)
• D) \(\mathbf { a } . \mathrm { A } = 1,280 , \mathrm {~B} = 0\)
• b. Profit \(= 102,400\)
• c. 1,280 units of \(\mathrm { A }\) and 0 units of \(\mathrm { B }\)

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Definitions:

Probability

A measurement of the likelihood or chance that a certain event will occur, expressed as a number between 0 and 1 (where 1 indicates certainty).

Utility

A measure of satisfaction or happiness that a consumer receives from consuming goods and services.

Expected Utility Function

A concept in economics and decision theory that represents an individual's preference for a set of possible outcomes based on a probability distribution.

Sure Payment

A fixed amount of money that is guaranteed to be paid under specified conditions.