Question

Ivanhoe's Wind Toys manufactures decorative kites, banners, and windsocks. During the month of January, Ivanhoe received orders for 4,000 Valentine’s Day banners and 1,300 Easter kites. Because several sewing machines are in the shop for repairs, Ivanhoe has only 1,200 sewing machine hours available for production of these orders. Each Valentine’s Day banner sells for $11. The banners take one hour to sew and have a total variable cost of $9 per banner. The Easter kites sell for $15. They take 15 minutes to sew and have a total variable cost of $14. (a) With only 1,200 sewing machine hours available, how many units should Ivanhoe produce for the below items?

Answer 1

Ivanhoe's Wind Toys should produce 1,200 Valentine's Day banners to maximize profit within the limit of 1,200 sewing machine hours, resulting in $2 contribution margin per unit. No Easter kites will be produced as they offer lower contribution margin and the available hours would be entirely used for banner production.

Step-by-step explanation:

Ivanhoe's Wind Toys must decide how many Valentine's Day banners and Easter kites to produce within the constraint of 1,200 sewing machine hours available for production. To calculate the optimal production mix, let's consider the contribution margin per unit for each product, which is the sale price minus the variable cost per unit.

For Valentine's Day banners:

• Selling price: $11
• Variable cost: $9
• Contribution margin per banner: $11 - $9 = $2 per banner
• Sewing time: 1 hour per banner

For Easter kites:

• Selling price: $15
• Variable cost: $14
• Contribution margin per kite: $15 - $14 = $1 per kite
• Sewing time: 0.25 hours (15 minutes) per kite

Given the higher contribution margin for banners, Ivanhoe should maximize the production of banners. With 1,200 hours, all hours can be dedicated to producing banners, yielding:

1,200 hours × 1 banner/hour = 1,200 banners.

No hours would remain to produce any kites, making the production number for kites 0 Easter kites.

It's important to note that Ivanhoe will not meet the entire demand for banners and will not start the production of kites due to amount of sewing time required and the contribution margin comparison. If other considerations such as fulfilling a minimum quantity of orders for kites or customer satisfaction over meeting demand for the Easter season are significant, Ivanhoe may need to adjust this straightforward profit-maximizing decision.

Answer 2

1300 Easter kites and 875 Valentine's banners

Step-by-step explanation:

Contribution per unit of Valentines day banner=11-9 =$2

Hours required for a unit of Valentines day banner = 1 hour

Contribution per unit of Easter kites = 15 -14 = $1

Hours required to sew Easter kite = 0.25

Contribution per hour for Easter Kite = 1*4 = $4

To maximize profit , Ivanhoe should produce

1300 Easter Kite.

Hours required for 1300 Easter Kite = 1300*.25=325 hours

The he can used the remaining hours (1200-325= 875) to produce 875 Valentines day banner

Over all contribution = (325 * 4) + (875*2)= 1300+1750=3050.

This is better than using all the available hours to produce 1200 Valentine's days banners and have an overall contribution =f 1200*2 = $2,400