17.07.2022 - 04:22

# Anne Sugar makes large ceramic pots for use in outdoor landscaping. She currently has two models, one square and the other round. Because of the size of Anne’s creations, only one pot can be fired in

Question:

Anne Sugar makes large ceramic pots for use in outdoor landscaping. She currently has two models, one square and the other round. Because of the size of Anne’s creations, only one pot can be fired in the kiln at a time. Information about each model follows:

 Square Round Sales price $70$90 Variable cost $15$20 Firing time 2.5 hours 3.5 hours

Assume that Anne can sell as many pots as she can create but that she is limited as to the number of hours that the kiln can be run.

Required:

Compute the contribution margin per unit and contribution margin per hour of firing time.

 Square Ceramic Pot Round Ceramic Pot Contribution Margin per Unit Contribution Margin per Hour
The maximum area Anne can afford is $850 /$25 per square foot = 34 square feet. Let the length of the patio be 3x and the width be 2x. The area of the rectangle is (3x)(2x) = 6x^2. We want to find the largest possible dimensions of the patio, so we need to maximize the area while keeping it under 34 square feet. Therefore, we set up the inequality 6x^2 ? 34, which simplifies to x^2 ? 17/3. Taking the square root of both sides, we get x ? ?(17/3). Since we want integer values for the length and width of the patio, we round down to the nearest whole number and get x = 2. Therefore, the dimensions of the largest patio Anne can afford are 6x2 and 4x2, or 12 feet by 8 feet.