Boylan Company manufactures two products-toaster ovens and bread machines.The following data are available: $$\begin{array} { | l | r | r | }
\hline & \text { Toaster Ovens } & \text { Bread Machines } \
\hline \text { Sales price } & \$ 60 & \$ 170 \
\hline \text { Variable costs } & \$ 50 & \$ 60 \
\hline
\end{array}$$ Boylan can manufacture six toaster ovens per machine hour and four bread machines per machine hour.Boylan's production capacity is 1600 machine hours per month.Marketing limitations indicate that Boylan can sell a maximum of 6000 toasters and 4100 bread machines per month.Which product and how many units should the company produce in a month to maximize profits? (Round machine hour per unit to two decimal places and your final answer to the nearest whole dollar.)

Question

Boylan Company manufactures two products-toaster ovens and bread machines.The following data are available: $$\begin{array} { | l | r | r | } 
\hline & \text { Toaster Ovens } & \text { Bread Machines } \
\hline \text { Sales price } & \$ 60 & \$ 170 \
\hline \text { Variable costs } & \$ 50 & \$ 60 \
\hline
\end{array}$$ Boylan can manufacture six toaster ovens per machine hour and four bread machines per machine hour.Boylan's production capacity is 1600 machine hours per month.Marketing limitations indicate that Boylan can sell a maximum of 6000 toasters and 4100 bread machines per month.Which product and how many units should the company produce in a month to maximize profits? (Round machine hour per unit to two decimal places and your final answer to the nearest whole dollar.)

Quizplus · Accepted Answer

To solve this problem, we need to use linear programming techniques. Let:

- x = number of toaster ovens produced
- y = number of bread machines produced

Then the objective function (what we want to maximize) is:

Profit = 50x + 70y

where 50 is the profit per toaster oven and 70 is the profit per bread machine.

There are two constraints:

1. Production capacity constraint:

6x + 4y ≤ 1600 (since Boylan can manufacture six toaster ovens per machine hour and four bread machines per machine hour, and the production capacity is 1600 machine hours per month)

2. Marketing limitations constraint:

x ≤ 6000 (since Boylan can sell a maximum of 6000 toasters per month)

y ≤ 4100 (since Boylan can sell a maximum of 4100 bread machines per month)

We can graph these constraints to find the feasible region:

The feasible region is the shaded area.

The corner points of the feasible region are (0,0), (1000,0), (6000/7,800/7), (3450,4100), and (6000,0).

We can then calculate the profit at each corner point:

- (0,0): Profit = 0
- (1000,0): Profit = 50(1000) + 0 = 50000
- (6000/7,800/7): Profit = 50(6000/7) + 70(800/7) ≈ 52714
- (3450,4100): Profit = 50(3450) + 70(4100) = 377500
- (6000,0): Profit = 50(6000) + 0 = 300000

Therefore, the maximum profit of $377500 is achieved by producing 3450 toaster ovens and 4100 bread machines.

Boylan Company Manufactures Two Products-Toaster Ovens and Bread Machines Boylan Can Manufacture Six Toaster Ovens Per Machine Hour and Data